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Longer titles found: Localization (commutative algebra) (view), Differential calculus over commutative algebras (view), List of commutative algebra topics (view), Combinatorial commutative algebra (view), Journal of Commutative Algebra (view), Homological conjectures in commutative algebra (view), Introduction to Commutative Algebra (view), Supercommutative algebra (view), Glossary of commutative algebra (view), Noncommutative algebraic geometry (view)

searching for Commutative algebra 133 found (713 total)

alternate case: commutative algebra

Éléments de mathématique (3,110 words) [view diff] case mismatch in snippet view article find links to article

(1989). Commutative Algebra: Chapters 1-7. Elements of Mathematics. Springer. ISBN 9783540642398. English paperback edition. Commutative Algebra: Chapters

CoCoA (361 words) [view diff] case mismatch in snippet view article find links to article

CoCoA (Computations in Commutative Algebra) is a free computer algebra system developed by the University of Genova, Italy, used to compute with numbers

List of lemmas (525 words) [view diff] no match in snippet view article find links to article

This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list

Generalized function (2,203 words) [view diff] no match in snippet view article find links to article

In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory

Reduced ring (817 words) [view diff] exact match in snippet view article find links to article

non-zero elements with square zero, that is, x2 = 0 implies x = 0. A commutative algebra over a commutative ring is called a reduced algebra if its underlying

Srinivasacharya Raghavan (450 words) [view diff] case mismatch in snippet view article find links to article

Society for many years. He was a coauthor of Homological Methods in Commutative Algebra. He retired as Senior Professor from the Tata Institute of Fundamental

Poisson ring (392 words) [view diff] exact match in snippet view article find links to article

important in studying the classical limit of quantum mechanics—the non-commutative algebra of operators on a Hilbert space has the Poisson algebra of functions

Lorenzo Ramero (308 words) [view diff] exact match in snippet view article find links to article

on commutative algebra, Grimoire d'Algèbre Commutative (in French), emphasizing the numerous connections and interactions between commutative algebra and

Graduate Texts in Mathematics (5,056 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-0-387-90125-1) Commutative Algebra I, Oscar Zariski, Pierre Samuel (1975, ISBN 978-0-387-90089-6) Commutative Algebra II, Oscar Zariski, Pierre

Functional-theoretic algebra (996 words) [view diff] exact match in snippet view article find links to article

products in terms of two linear functionals. In general, it is a non-commutative algebra. It becomes commutative when the two functionals are the same. Let

Michel André (mathematician) (234 words) [view diff] exact match in snippet view article

1936 – 9 July 2009) was a Swiss mathematician, specializing in non-commutative algebra and its applications to topology. He is known for André–Quillen cohomology

Yoshiro Mori (mathematician) (53 words) [view diff] exact match in snippet view article

Yoshiro Mori is a Japanese mathematician working on commutative algebra who introduced the Mori–Nagata theorem and whose work led to Mori domains.[when

Goldman domain (635 words) [view diff] case mismatch in snippet view article find links to article

Kaplansky, Irving. Commutative Algebra. The University of Chicago Press, 1974, pp. 12, 13. Kaplansky, Irving. Commutative Algebra. The University of Chicago

Dunsink Observatory (864 words) [view diff] exact match in snippet view article find links to article

who, amongst other things, discovered quaternions, the first non-commutative algebra form, while walking from the observatory to the city with his wife

Reynolds operator (996 words) [view diff] exact match in snippet view article find links to article

taken over a compact group or reductive algebraic group acting on a commutative algebra, such as a ring of polynomials. Reynolds operators were introduced

Martin Kreuzer (480 words) [view diff] case mismatch in snippet view article find links to article

Computational Commutative Algebra I, by Martin Kreuzer and Lorenzo Robbiano, Heidelberg, Springer-Verlag 2000, ISBN 978-3-540-67733-8. Computational Commutative Algebra

Zariski's main theorem (1,601 words) [view diff] exact match in snippet view article find links to article

structure of quasi-finite morphisms of schemes. Several results in commutative algebra imply the geometric forms of Zariski's main theorem, including: A

Phillip Griffith (149 words) [view diff] exact match in snippet view article find links to article

emeritus at University of Illinois at Urbana-Champaign who works on commutative algebra and ring theory. He received his PhD from the University of Houston

Exalcomm (1,998 words) [view diff] exact match in snippet view article find links to article

In algebra, Exalcomm is a functor classifying the extensions of a commutative algebra by a module. More precisely, the elements of Exalcommk(R,M) are isomorphism

Finitely generated module (2,878 words) [view diff] exact match in snippet view article find links to article

ring R is Noetherian. Both facts imply that a finitely generated commutative algebra over a Noetherian ring is again a Noetherian ring. More generally

Fuzzy sphere (582 words) [view diff] exact match in snippet view article find links to article

replaces an infinite-dimensional commutative algebra by a j 2 {\displaystyle j^{2}} -dimensional non-commutative algebra. The simplest way to see this sphere

Bicomplex number (1,806 words) [view diff] exact match in snippet view article find links to article

quadratic form in the first component. The bicomplex numbers form a commutative algebra over C of dimension two that is isomorphic to the direct sum of algebras

Miles Reid (331 words) [view diff] case mismatch in snippet view article find links to article

known books: Undergraduate Algebraic Geometry and Undergraduate Commutative Algebra. Reid was elected a Fellow of the Royal Society in 2002. In the same

Normal scheme (1,087 words) [view diff] case mismatch in snippet view article find links to article

of singularities Eisenbud, D. Commutative Algebra (1995). Springer, Berlin. Theorem 11.5 Eisenbud, D. Commutative Algebra (1995). Springer, Berlin. Corollary

Dual Steenrod algebra (818 words) [view diff] exact match in snippet view article find links to article

through an algebraic operation (dualization), there is an associated commutative algebra from the noncommutative Steenrod algebras called the dual Steenrod

Richard P. Stanley (442 words) [view diff] case mismatch in snippet view article find links to article

Combinatorics (1986–1999). He is also the author of Combinatorics and Commutative Algebra (1983) and well over 200 research articles in mathematics. He has

Noetherian ring (2,773 words) [view diff] exact match in snippet view article find links to article

homomorphism of a Noetherian ring is Noetherian. Every finitely-generated commutative algebra over a commutative Noetherian ring is Noetherian. (This follows from

Nilpotent (1,210 words) [view diff] case mismatch in snippet view article find links to article

127. Matsumura, Hideyuki (1970). "Chapter 1: Elementary Results". Commutative Algebra. W. A. Benjamin. p. 6. ISBN 978-0-805-37025-6. Atiyah, M. F.; MacDonald

Field (mathematics) (10,305 words) [view diff] exact match in snippet view article

domain: (f ⋅ g)(x) = f(x) ⋅ g(x). This makes these functions a F-commutative algebra. For having a field of functions, one must consider algebras of functions

Martha K. Smith (614 words) [view diff] exact match in snippet view article find links to article

University of Texas at Austin. She has made contributions to non-commutative algebra and as well as to mathematics education. Smith received a B.A. in

Condensed mathematics (811 words) [view diff] exact match in snippet view article find links to article

Kedlaya described condensed mathematics as "technology for doing commutative algebra over topological rings." The fundamental idea in the development

Hilbert–Kunz function (411 words) [view diff] case mismatch in snippet view article find links to article

This article is also found on pages 485-525 of the Springer volume "Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of

Hyperconnected space (1,802 words) [view diff] case mismatch in snippet view article find links to article

Nicolas (1989). Commutative Algebra: Chapters 1-7. Springer. p. 95. ISBN 978-3-540-64239-8. Bourbaki, Nicolas (1989). Commutative Algebra: Chapters 1-7

Ian G. Macdonald (644 words) [view diff] case mismatch in snippet view article find links to article

ISBN 0-8218-0770-6 MR1488699 Atiyah, M. F.; Macdonald, I. G. Introduction to Commutative Algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills,

Kochen–Specker theorem (3,030 words) [view diff] exact match in snippet view article find links to article

commuting subalgebras of the algebra of these observables in one commutative algebra, assumed to represent the classical structure of the hidden-variables

Derivation (differential algebra) (1,066 words) [view diff] exact match in snippet view article

mathematics, Springer-Verlag, ISBN 3-540-64243-9. Eisenbud, David (1999), Commutative algebra with a view toward algebraic geometry (3rd. ed.), Springer-Verlag

Global dimension (725 words) [view diff] exact match in snippet view article find links to article

theorem opened the door to application of homological methods to commutative algebra. Auslander, Maurice (1955). "On the dimension of modules and algebras

Associated graded ring (982 words) [view diff] case mismatch in snippet view article find links to article

Ch. VIII, a paragraph after Theorem 1. Eisenbud, David (1995). Commutative Algebra. Graduate Texts in Mathematics. Vol. 150. New York: Springer-Verlag

Symbolic-numeric computation (188 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-3-540-65466-7. Robbiano, Lorenzo; Abbott, John (2009). Approximate Commutative Algebra. Springer. ISBN 978-3-211-99313-2. Langer, Ulrich; Paule, Peter,

Normal (580 words) [view diff] exact match in snippet view article find links to article

theory Normal polytopes, in polyhedral geometry and computational commutative algebra Normal ring, a reduced ring whose localizations at prime ideals are

Graduate Studies in Mathematics (4,546 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-1-4704-7419-5) 233 Commutative Algebra, Andrea Ferretti (2023, ISBN 978-1-4704-7434-8) 234 Homological Methods in Commutative Algebra, Andrea Ferretti (2023

Cyclic homology (1,544 words) [view diff] exact match in snippet view article find links to article

referred to as the periodicity sequence. Cyclic cohomology of the commutative algebra A of regular functions on an affine algebraic variety over a field

Nakayama (140 words) [view diff] exact match in snippet view article find links to article

Station (Hyogo) Nakayamadaira-Onsen Station Nakayama lemma, a lemma in commutative algebra This disambiguation page lists articles associated with the title

Topological module (343 words) [view diff] case mismatch in snippet view article find links to article

Atiyah, Michael Francis; MacDonald, I.G. (1969). Introduction to Commutative Algebra. Westview Press. ISBN 978-0-201-40751-8. Kuz'min, L. V. (1993). "Topological

Prime ideal (2,748 words) [view diff] case mismatch in snippet view article find links to article

Springer. ISBN 0-387-95385-X. Reid, Miles (1996). Undergraduate Commutative Algebra. Cambridge University Press. ISBN 0-521-45889-7. Lam First Course

NNL (134 words) [view diff] exact match in snippet view article find links to article

League had disbanded Noether normalization lemma — a theorem in commutative algebra No net loss – an environmental policy approach This disambiguation

Rational homotopy theory (4,039 words) [view diff] exact match in snippet view article find links to article

let X be any space whose rational cohomology ring is a free graded-commutative algebra (a tensor product of a polynomial ring on generators of even degree

Todorov surface (93 words) [view diff] exact match in snippet view article find links to article

(1988), "On the moduli of Todorov surfaces", Algebraic geometry and commutative algebra, vol. I, Tokyo: Kinokuniya, pp. 313–355, MR 0977767 Todorov, Andrei

M-sequence (60 words) [view diff] exact match in snippet view article find links to article

M-sequence may refer to: Regular sequence, which is an important topic in commutative algebra. A maximum length sequence, which is a type of pseudorandom binary

Deformation quantization (1,102 words) [view diff] exact match in snippet view article find links to article

rules for how to deform the "classical" commutative algebra of observables to a quantum non-commutative algebra of observables. The basic setup in deformation

Going Up (124 words) [view diff] exact match in snippet view article find links to article

Going Up may refer to: Going up and going down, terms in commutative algebra which refer to certain properties of chains of prime ideals in integral extensions

Projectivization (336 words) [view diff] exact match in snippet view article find links to article

procedure that associates a projective variety Proj S with a graded commutative algebra S (under some technical restrictions on S). If S is the algebra of

Clifford's theorem on special divisors (734 words) [view diff] exact match in snippet view article find links to article

Eisenbud, David (2005). The Geometry of Syzygies. A second course in commutative algebra and algebraic geometry. Graduate Texts in Mathematics. Vol. 229.

Anticommutative property (606 words) [view diff] exact match in snippet view article find links to article

Wiktionary, the free dictionary. Gainov, A.T. (2001) [1994], "Anti-commutative algebra", Encyclopedia of Mathematics, EMS Press. Which references the Original

Height (disambiguation) (206 words) [view diff] exact match in snippet view article

properties of an element Height (ring theory), a measurement in commutative algebra Height (triangle) or altitude Height function, a function that quantifies

Going Down (270 words) [view diff] exact match in snippet view article find links to article

XXXTentacion from ?, 2018 Going up and going down, a concept in commutative algebra Oral sex Get down, a dance move in African and African diaspora culture

Norman Steenrod (517 words) [view diff] no match in snippet view article find links to article

finer invariant. The Steenrod cohomology operations form a (non-commutative) algebra under composition, known as the Steenrod algebra. His book The Topology

Comodule (814 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathcal {A}}^{*}} is a commutative ring, and the setting of commutative algebra provides more tools for studying its structure. If M is a (right)

Egbert Brieskorn (326 words) [view diff] exact match in snippet view article find links to article

Erhard Scholz. "Egbert Brieskorn, 1936–2013 :: commalg.org :: the commutative algebra community". commalg.org. 16 July 2013. Retrieved 2013-07-16. Egbert

Frobenius splitting (164 words) [view diff] exact match in snippet view article find links to article

JSTOR 1971368, MR 0799251 Conference on Frobenius splitting in algebraic geometry, commutative algebra, and representation theory at Michigan, 2010. v t e

Vasudevan Srinivas (446 words) [view diff] exact match in snippet view article find links to article

subfields of interest include the areas of algebraic cycles, K-theory, commutative algebra and positive characteristic methods. He is well-known for the Bloch-Srinivas

Simplicial sphere (515 words) [view diff] exact match in snippet view article find links to article

1016/0095-8956(71)90042-6. Stanley, Richard (1996). Combinatorics and commutative algebra. Progress in Mathematics. Vol. 41 (Second ed.). Boston: Birkhäuser

Grade (581 words) [view diff] exact match in snippet view article find links to article

of plane angles Grade (ring theory), a cohomological invariant in commutative algebra Graded (mathematics), with several meanings Graded poset, a partially

Gelfand–Kirillov dimension (332 words) [view diff] exact match in snippet view article find links to article

is finite. The Gelfand–Kirillov dimension of a finitely generated commutative algebra A over a field is the Krull dimension of A (or equivalently the transcendence

Filtered algebra (812 words) [view diff] exact match in snippet view article find links to article

of differential operators. The associated graded algebra is the commutative algebra of smooth functions on the cotangent bundle T ∗ M {\displaystyle

Fyodor Zak (187 words) [view diff] exact match in snippet view article find links to article

a theorem of G. Scorza", Geometric and combinatorial aspects of commutative algebra (Messina, 1999), Lecture Notes in Pure and Appl. Math., vol. 217

Fuzzy mathematics (932 words) [view diff] case mismatch in snippet view article find links to article

vol. 182. Springer-Verlag. Mordeson, J.N., Malik, D.S (1998) Fuzzy Commutative Algebra. World Scientific. Chang, C.L. (1968) "Fuzzy topological spaces"

Gerstenhaber algebra (490 words) [view diff] exact match in snippet view article find links to article

defined on differential forms. A Gerstenhaber algebra is a graded-commutative algebra with a Lie bracket of degree −1 satisfying the Poisson identity.

Algebraic closure (992 words) [view diff] exact match in snippet view article find links to article

(1991) p.21 M. F. Atiyah and I. G. Macdonald (1969). Introduction to commutative algebra. Addison-Wesley publishing Company. pp. 11–12. Kaplansky (1972) pp

Split exact sequence (493 words) [view diff] case mismatch in snippet view article find links to article

Springer, ISBN 9783319194226 Sharp, R. Y., Rodney (2001), Steps in Commutative Algebra, 2nd ed., London Mathematical Society Student Texts, Cambridge University

Integral (disambiguation) (238 words) [view diff] exact match in snippet view article

according to which a nation is an organic unity Integrality, in commutative algebra, the notions of an element integral over a ring Integration (disambiguation)

Rigidity (K-theory) (530 words) [view diff] exact match in snippet view article

Henselian local rings and Henselian pairs", Algebraic K-theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989), Contemp

Gonality of an algebraic curve (408 words) [view diff] exact match in snippet view article find links to article

Eisenbud, David (2005). The Geometry of Syzygies. A second course in commutative algebra and algebraic geometry. Graduate Texts in Mathematics. Vol. 229.

Real-valued function (993 words) [view diff] exact match in snippet view article find links to article

{F}}(X,{\mathbb {R} })} may be turned into a vector space and a commutative algebra over the reals with the following operations: f + g : x ↦ f ( x )

Finite morphism (855 words) [view diff] exact match in snippet view article find links to article

proper. This follows from the going up theorem of Cohen-Seidenberg in commutative algebra. Finite morphisms have finite fibers (that is, they are quasi-finite)

Mutation (algebra) (588 words) [view diff] exact match in snippet view article

non-zero weight is again a Bernstein algebra. A Jordan algebra is a commutative algebra satisfying the Jordan identity ( x y ) ( x x ) = x ( y ( x x ) )

David A. Cox (412 words) [view diff] exact match in snippet view article find links to article

algorithms: an introduction to computational algebraic geometry and commutative algebra, 3rd. edition, Springer Verlag 2007 David A. Cox, John Little, and

Andrei Zelevinsky (584 words) [view diff] exact match in snippet view article find links to article

Seminal Contribution to Research (2018) News on website for the commutative algebra community "Medal-winning graduates of the Moscow Mathematical School

Commutative property (1,504 words) [view diff] exact match in snippet view article find links to article

always commutative.) However, in the case of algebras, the phrase "commutative algebra" refers only to associative algebras that have a commutative multiplication

Volterra equation (68 words) [view diff] exact match in snippet view article find links to article

over an operator-valued function, such as a function into a non-commutative algebra. This disambiguation page lists mathematics articles associated with

Hiroshi Umemura (mathematician) (349 words) [view diff] case mismatch in snippet view article

First Differential Equation of Painlevé", Algebraic Geometry and Commutative Algebra, Elsevier, pp. 771–789, doi:10.1016/b978-0-12-348032-3.50015-3, ISBN 9780123480323

Ferrero–Washington theorem (618 words) [view diff] exact match in snippet view article find links to article

μ-invariants of Z1-extensions", Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki, Tokyo: Kinokuniya, pp. 1–11, MR 0357371

Clay Research Award (71 words) [view diff] exact match in snippet view article find links to article

topology." 2021 Bhargav Bhatt "For his groundbreaking achievements in commutative algebra, arithmetic algebraic geometry, and topology in the p-adic setting

Spectrum (disambiguation) (973 words) [view diff] exact match in snippet view article

dual object Spectrum of a ring, the set of its prime ideals, in commutative algebra Spectrum (brand), a brand name used by Charter Communications for

Torsionless module (658 words) [view diff] exact match in snippet view article find links to article

Proposition 8. Lam 1999, p 146. Chapter VII of Bourbaki, Nicolas (1998), Commutative algebra (2nd ed.), Springer Verlag, ISBN 3-540-64239-0 Lam, Tsit Yuen (1999)

Determinantal variety (723 words) [view diff] case mismatch in snippet view article find links to article

1016/0001-8708(78)90037-3. Miller, Ezra; Sturmfels, Bernd (2005). Combinatorial Commutative Algebra. Graduate Texts in Mathematics. Vol. 227. Springer. ISBN 978-0-387-23707-7

Dehn–Sommerville equations (780 words) [view diff] case mismatch in snippet view article find links to article

Springer, 2003 ISBN 0-387-00424-6 Richard P. Stanley, Combinatorics and Commutative Algebra. Second edition. Progress in Mathematics, 41. Birkhäuser Boston,

Complex number (11,795 words) [view diff] exact match in snippet view article find links to article

structure that is simultaneously an algebraically closed field, a commutative algebra over the reals, and a Euclidean vector space of dimension two. A

Gorenstein scheme (679 words) [view diff] case mismatch in snippet view article find links to article

20 and 5.22.) (Kollár 2013, Example 3.6.) Eisenbud, David (1995), Commutative Algebra with a View toward Algebraic Geometry, Graduate Texts in Mathematics

Upper bound theorem (709 words) [view diff] case mismatch in snippet view article find links to article

shellability and h-vectors. Stanley, Richard (1996). Combinatorics and Commutative Algebra. Birkhäuser Boston. p. 164. ISBN 0-8176-3836-9. Stanley, Richard

Linear topology (365 words) [view diff] exact match in snippet view article find links to article

Journal. 24 (2): 219–286. arXiv:2012.15431. doi:10.17323/1609-4514-2024-24-2-219-286. Bourbaki, N. (1972). Commutative algebra (Vol. 8). Hermann. v t e

Kontsevich invariant (938 words) [view diff] exact match in snippet view article find links to article

diagrams. In the special case where X is an interval I, A(X) will be a commutative algebra. Viewing A(S1) as the algebra with multiplication as connected sums

ACC (1,346 words) [view diff] exact match in snippet view article find links to article

change caused by humans Ascending chain condition, a condition in commutative algebra ACC (complexity), a hierarchy of complexity classes used in circuit

Leroy P. Steele Prize (2,239 words) [view diff] exact match in snippet view article find links to article

Algorithms, which has made algebraic geometry and computational commutative algebra accessible not just to mathematicians but to students and researchers

Nicolas Bourbaki (11,924 words) [view diff] exact match in snippet view article find links to article

unnumbered books treating modern areas of research (Lie groups, commutative algebra), each presupposing the first half as a shared foundation but without

Siegfried Bosch (290 words) [view diff] exact match in snippet view article find links to article

missing publisher (link) Bosch, S. (2013). Algebraic geometry and commutative algebra. London: Springer. ISBN 978-1-4471-4829-6. OCLC 821020969. "Algebra"

Salomon Bochner (999 words) [view diff] exact match in snippet view article find links to article

J.: Princeton University Press. Bochner, S. (1938). Lectures on commutative algebra. Ann Arbor, Mich.: Planographed by Edwards Brothers, inc; lectures

Budapest Semesters in Mathematics (484 words) [view diff] case mismatch in snippet view article find links to article

Topics in Analysis Complex Functions Combinatorics 1 Combinatorics 2 Commutative Algebra Conjecture and Proof Functional Analysis Elementary Problem Solving

Graded-symmetric algebra (215 words) [view diff] case mismatch in snippet view article find links to article

and zero elsewhere is the exterior algebra of V. David Eisenbud, Commutative Algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics

Simple function (845 words) [view diff] exact match in snippet view article find links to article

collection of all simple functions on a given measurable space forms a commutative algebra over C {\displaystyle \mathbb {C} } . If a measure μ {\displaystyle

List of open-source software for mathematics (1,604 words) [view diff] case mismatch in snippet view article find links to article

it is no longer restricted to physicists. CoCoA (COmputations in COmmutative Algebra) is open-source software used for computing multivariate polynomials

Mara Neusel (642 words) [view diff] case mismatch in snippet view article find links to article

Mathematical Society in Lubbock, Texas as well as a special session on "Commutative Algebra and Algebraic Geometry" at the 40th Anniversary Celebration of the

Moss Sweedler (737 words) [view diff] exact match in snippet view article find links to article

finite characteristic. From 1965 to the mid 1980s Sweeder worked on commutative algebra and related disciplines. Since the mid 1980s Sweedler has worked

Donal O'Shea (349 words) [view diff] exact match in snippet view article find links to article

algorithms: an introduction to computational algebraic geometry and commutative algebra, 3rd. edition, Springer Verlag, 2007. "Donal B. O'Shea". www.encyclopedia

Kruskal–Katona theorem (973 words) [view diff] exact match in snippet view article find links to article

1016/j.disc.2019.111801 Stanley, Richard (1996), Combinatorics and commutative algebra, Progress in Mathematics, vol. 41 (2nd ed.), Boston, MA: Birkhäuser

Snake lemma (1,592 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-0-387-95385-4. Atiyah, M.F.; Macdonald, I. G. (1969). Introduction to Commutative Algebra. Addison–Wesley. ISBN 0-201-00361-9. Hilton, P.; Stammbach, U. (1997)

Unique factorization domain (1,800 words) [view diff] exact match in snippet view article find links to article

Algebra. Prentice Hall. ISBN 978-0-13-241377-0. Bourbaki, N. (1972). Commutative algebra. Paris, Hermann; Reading, Mass., Addison-Wesley Pub. Co. ISBN 9780201006445

Exact sequence (2,577 words) [view diff] case mismatch in snippet view article find links to article

Berlin: Springer. p. 179. ISBN 0-387-94426-5. Eisenbud, David (1995). Commutative Algebra: with a View Toward Algebraic Geometry. Springer-Verlag New York

Nakano vanishing theorem (330 words) [view diff] exact match in snippet view article find links to article

weakly 1-complete manifolds". Number theory, algebraic geometry and commutative algebra — in honor of Yasuo Akizuki. Kinokuniya. pp. 169–179. Nakano, Shigeo

Weil restriction (1,139 words) [view diff] exact match in snippet view article find links to article

but does not generalize it, since the ring of Witt vectors on a commutative algebra A is not in general an A-algebra. Bosch, Siegfried; Lütkebohmert

Zariski–Riemann space (813 words) [view diff] exact match in snippet view article find links to article

ISSN 0002-9904, MR 0011573 Zariski, Oscar; Samuel, Pierre (1975), Commutative algebra. Vol. II, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90171-8

Eilenberg–Mazur swindle (1,099 words) [view diff] exact match in snippet view article find links to article

doi:10.1215/ijm/1255637479, MR 0143789 Eisenbud, David (1995), Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics

Homogeneous coordinate ring (1,275 words) [view diff] case mismatch in snippet view article find links to article

American Mathematical Society, Vol. 13, No. 3 (Jul., 2000), pp. 651–664. Oscar Zariski and Pierre Samuel, Commutative Algebra Vol. II (1960), pp. 168–172.

Absolute value (algebra) (1,403 words) [view diff] case mismatch in snippet view article

of Valuations". Retrieved 2023-01-28. Bourbaki, Nicolas (1972). Commutative Algebra. Addison-Wesley. Cassels, J.W.S. (1986). Local Fields. London Mathematical

Conic bundle (666 words) [view diff] case mismatch in snippet view article find links to article

(second ed.). Springer-Verlag. ISBN 0-387-94680-2. David Eisenbud (1999). Commutative Algebra with a View Toward Algebraic Geometry. Springer-Verlag. ISBN 0-387-94269-6

Michael Atiyah (8,832 words) [view diff] exact match in snippet view article find links to article

Atiyah's collected papers include most of his work, except for his commutative algebra textbook; the first five volumes are divided thematically and the

Polyvector field (698 words) [view diff] exact match in snippet view article find links to article

{\displaystyle ({\mathfrak {X}}^{\bullet }(M),\wedge )} into a graded commutative algebra. Similarly, the Lie bracket of vector fields extends to the so-called

Archimedean group (1,186 words) [view diff] case mismatch in snippet view article find links to article

property. Alajbegovic, J.; Mockor, J. (1992), Approximation Theorems in Commutative Algebra: Classical and Categorical Methods, NATO ASI Series. Series D, Behavioural

Tarbiat Modares University (1,110 words) [view diff] case mismatch in snippet view article find links to article

Department of Pure Mathematics include Algebra (Group Theory and Non-Commutative Algebra), Analysis (Harmonic and Functional Analysis), Dynamical systems

Breakthrough Prize in Mathematics (1,432 words) [view diff] exact match in snippet view article find links to article

Murphy Xinwen Zhu 2021 Bhargav Bhatt – "For outstanding work in commutative algebra and arithmetic algebraic geometry, particularly on the development

Almost all (2,577 words) [view diff] case mismatch in snippet view article find links to article

Schoutens, Hans (2 August 2010). The Use of Ultraproducts in Commutative Algebra. Lecture Notes in Mathematics. Vol. 1999. Springer. p. 8. doi:10

Artinian module (1,115 words) [view diff] case mismatch in snippet view article find links to article

"Chapter 6. Chain conditions; Chapter 8. Artin rings". Introduction to Commutative Algebra. Westview Press. ISBN 978-0-201-40751-8. Cohn, P.M. (1997). "Cyclic

Torsion (algebra) (1,660 words) [view diff] exact match in snippet view article

coefficient theorem Roman 2008, p. 115, §4 Ernst Kunz, "Introduction to Commutative algebra and algebraic geometry", Birkhauser 1985, ISBN 0-8176-3065-1 Irving

Free object (2,027 words) [view diff] exact match in snippet view article find links to article

free objects include: free algebra free associative algebra free commutative algebra free category free strict monoidal category free group free abelian

List of women in mathematics (23,282 words) [view diff] exact match in snippet view article find links to article

mathematics textbooks Melody Chan, American expert in combinatorial commutative algebra, graph theory, and tropical geometry Sun-Yung Alice Chang (born 1948)

Closed graph theorem (1,926 words) [view diff] exact match in snippet view article find links to article

hold Zariski's main theorem – Theorem of algebraic geometry and commutative algebra "The closed graph theorem in various categories". 21 November 2012

Iwasawa algebra (1,182 words) [view diff] case mismatch in snippet view article find links to article

classified up to so-called pseudo-null modules. Bourbaki, Nicolas (1972), Commutative Algebra, Paris: Hermann, Theorems 4, 5, §VII.4.4. Coates, John; Schneider

Alexander duality (1,432 words) [view diff] case mismatch in snippet view article find links to article

2001 [1994] Miller, Ezra; Sturmfels, Bernd (2005). Combinatorial Commutative Algebra. Graduate Texts in Mathematics. Vol. 227. New York, NY: Springer-Verlag

Dual abelian variety (1,617 words) [view diff] case mismatch in snippet view article find links to article

(2017). Abelian Varieties (PDF). p. 38. Eisenbud, David (1995). Commutative Algebra with a View Toward Algebraic Geometry. Springer-Verlag. p. 521.

Tor functor (2,068 words) [view diff] exact match in snippet view article find links to article

commutative R-algebras A and B, TorR *(A,B) has the structure of a graded-commutative algebra over R. Moreover, elements of odd degree in the Tor algebra have

Israel Kleiner (mathematician) (694 words) [view diff] exact match in snippet view article

Berman, and B. Koichu, Sense Publishers, 2009, pp. 31–50 The roots of commutative algebra in algebraic number theory, Mathematics Magazine, Vol. 68, 1995,

Complementarity (physics) (3,047 words) [view diff] exact match in snippet view article

"astounding simplicity", by describing physical quantities using non-commutative algebra. This mathematical expression of complementarity builds on the work

Hyperbolic quaternion (2,107 words) [view diff] exact match in snippet view article find links to article

the 1890s Richard Dedekind had introduced the ring concept into commutative algebra, and the vector space concept was being abstracted by Giuseppe Peano