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Longer titles found: Structure theorem for Gaussian measures (view), Structure theorem for finitely generated modules over a principal ideal domain (view), Cohen structure theorem (view), Graph structure theorem (view), Chevalley's structure theorem (view)

searching for Structure theorem 59 found (120 total)

alternate case: structure theorem

Composition algebra (1,319 words) [view diff] no match in snippet view article find links to article

In mathematics, a composition algebra A over a field K is a not necessarily associative algebra over K together with a nondegenerate quadratic form N that
Fractional ideal (1,611 words) [view diff] exact match in snippet view article find links to article
I = 1 α J {\displaystyle I={\frac {1}{\alpha }}J} Another useful structure theorem is that integral fractional ideals are generated by up to 2 elements
Divisible group (1,422 words) [view diff] no match in snippet view article find links to article
In mathematics, specifically in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided
Dedekind group (399 words) [view diff] exact match in snippet view article find links to article
investigated them in (Dedekind 1897), proving a form of the above structure theorem (for finite groups). He named the non-abelian ones after William Rowan
Semigroup (4,714 words) [view diff] exact match in snippet view article find links to article
These semigroups have applications to commutative algebra. There is a structure theorem for commutative semigroups in terms of semilattices. A semilattice
Graph of groups (827 words) [view diff] no match in snippet view article find links to article
In geometric group theory, a graph of groups is an object consisting of a collection of groups indexed by the vertices and edges of a graph, together with
Classification of Clifford algebras (2,420 words) [view diff] exact match in snippet view article find links to article
complex Weyl spinor is an element of Δ+ n (respectively, Δ− n). The structure theorem is simple to prove inductively. For base cases, Cl0(C) is simply C
Cone of curves (1,007 words) [view diff] no match in snippet view article find links to article
In mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety X {\displaystyle X} is a combinatorial invariant of importance
Injective module (3,919 words) [view diff] no match in snippet view article find links to article
In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties
Stinespring dilation theorem (2,113 words) [view diff] exact match in snippet view article find links to article
operator map of the form T ↦ V*TV. Moreover, Stinespring's theorem is a structure theorem from a C*-algebra into the algebra of bounded operators on a Hilbert
Mordell–Weil group (1,164 words) [view diff] exact match in snippet view article find links to article
) {\displaystyle A(K)} is the Mordell–Weil grouppg 207. The main structure theorem about this group is the Mordell–Weil theorem which shows this group
Robert Ellis (mathematician) (324 words) [view diff] exact match in snippet view article
leading to a strengthening with an alternate proof of the Furstenberg structure theorem. He was the author or coauthor of about 40 research publications.
Stahl's theorem (411 words) [view diff] exact match in snippet view article find links to article
simplified proof of Stahl's theorem. In 2023, Otte Heinävaara proved a structure theorem for Hermitian matrices introducing tracial joint spectral measures
Topological dynamics (449 words) [view diff] exact match in snippet view article find links to article
George Birkhoff is considered to be the founder of the field. A structure theorem for minimal distal flows proved by Hillel Furstenberg in the early
Gorenstein ring (1,664 words) [view diff] exact match in snippet view article find links to article
Gorenstein if and only if it is a complete intersection. There is also a structure theorem for Gorenstein rings of codimension 3 in terms of the Pfaffians of
Peter B. Kronheimer (575 words) [view diff] exact match in snippet view article find links to article
They then went on to develop these tools further and established a structure theorem for Donaldson's polynomial invariants using Kronheimer–Mrowka basic
Characterization (mathematics) (1,517 words) [view diff] exact match in snippet view article
of matrices, the Jordan Canonical Form is a characterization, or structure theorem, for complex matrices, and the spectral theorem is likewise for symmetric
Ofer Gabber (210 words) [view diff] case mismatch in snippet view article find links to article
Press, 2010; 2015, 2nd edition Gabber rigidity Almost ring theory t-structure Theorem of absolute purity Ofer Gabber at the Mathematics Genealogy Project
Triangular decomposition (1,610 words) [view diff] exact match in snippet view article find links to article
reported experimental data in his 1987 pioneer article titled "A zero structure theorem for polynomial equations solving". To put this work into context,
Abelian variety (3,158 words) [view diff] exact match in snippet view article find links to article
is a product of elliptic curves, up to an isogeny. One important structure theorem of abelian varieties is Matsusaka's theorem. It states that over an
Leopold Kronecker (1,402 words) [view diff] exact match in snippet view article find links to article
proved completely much later by David Hilbert). He also introduced the structure theorem for finitely-generated abelian groups. Kronecker studied elliptic
Comodule over a Hopf algebroid (732 words) [view diff] exact match in snippet view article find links to article
\Gamma )} of the Hopf-algebroid is an abelian category. There is a structure theorem pg 7 relating comodules of Hopf-algebroids and modules of presheaves
Circle group (2,078 words) [view diff] exact match in snippet view article find links to article
isomorphic to ⁠ Q / Z {\displaystyle \mathbb {Q} /\mathbb {Z} } ⁠. The structure theorem for divisible groups and the axiom of choice together tell us that
Luc Illusie (982 words) [view diff] exact match in snippet view article find links to article
particular were the key tool in Grothendieck's proof of his existence and structure theorem for infinitesimal deformations of Barsotti–Tate groups, an ingredient
Ben Green (mathematician) (1,331 words) [view diff] exact match in snippet view article
group theory. In particular, jointly with Terence Tao, they proved a structure theorem for approximate groups, generalising the Freiman-Ruzsa theorem on
Rami Grossberg (577 words) [view diff] exact match in snippet view article find links to article
of Fuchs and Salce in the theory of modules; with Hart, proving a structure theorem for L ω 1 , ω {\displaystyle {\mathit {L}}_{\omega _{1},\omega }}
Locally compact abelian group (944 words) [view diff] exact match in snippet view article find links to article
map. Any finite abelian group, with the discrete topology. By the structure theorem for finite abelian groups, all such groups are products of cyclic
Reeb stability theorem (798 words) [view diff] no match in snippet view article find links to article
stability results: In the presence of a certain transverse geometric structure: Theorem: Let F {\displaystyle F} be a complete conformal foliation of codimension
Casson handle (985 words) [view diff] exact match in snippet view article find links to article
only in the way the boundary is attached to the interior. Freedman's structure theorem can be used to prove the h-cobordism theorem for 5-dimensional topological
Planar graph (4,541 words) [view diff] exact match in snippet view article find links to article
graphs also have treewidth and branch-width O(√n). The planar product structure theorem states that every planar graph is a subgraph of the strong graph product
Measure-preserving dynamical system (3,592 words) [view diff] case mismatch in snippet view article find links to article
Weiss, Benjamin (2019). "From Odometers to Circular Systems: A Global Structure Theorem". Journal of Modern Dynamics. 15: 345–423. arXiv:1703.07093. doi:10
Gauss–Manin connection (1,100 words) [view diff] exact match in snippet view article find links to article
results and discussion of open problems (Gives a quick sketch of main structure theorem of Gauss–Manin connections) Barrientos, Ivan, The Gauss-Manin connection
N-ary group (1,167 words) [view diff] exact match in snippet view article find links to article
an n-ary semigroup which is also an n-ary quasigroup. Post gave a structure theorem for an n-ary group in terms of an associated group.: 245-246  In the
Serre's inequality on height (452 words) [view diff] exact match in snippet view article find links to article
inequality, we can assume A {\displaystyle A} is complete. Then by Cohen's structure theorem, we can write A = A 1 / a 1 A 1 {\displaystyle A=A_{1}/a_{1}A_{1}}
Strong product of graphs (1,316 words) [view diff] exact match in snippet view article find links to article
Wood, David R.; Yi, Wendy (2022), "An improved planar graph product structure theorem", Electronic Journal of Combinatorics, 29 (2), Paper No. 2.51, arXiv:2108
Étale morphism (2,493 words) [view diff] exact match in snippet view article find links to article
\mathbb {A} _{Y}^{n}} . This is the étale analogue version of the structure theorem on submersions. Purity (algebraic geometry) fr: Trésor de la langue
Finite field (7,535 words) [view diff] exact match in snippet view article find links to article
{\displaystyle q-1} is the lowest possible value for k {\displaystyle k} . The structure theorem of finite abelian groups implies that this multiplicative group is
Intersection type (2,394 words) [view diff] no match in snippet view article find links to article
(2000). "Dependently typed records for representing mathematical structure". Theorem Proving in Higher Order Logics, 13th International Conference. TPHOLs
Peter–Weyl theorem (2,480 words) [view diff] exact match in snippet view article find links to article
From the Peter–Weyl theorem, one can deduce a significant general structure theorem. Let G be a compact topological group, which we assume Hausdorff.
Singular submodule (974 words) [view diff] no match in snippet view article find links to article
class of rings whose maximal right ring of quotients have a certain structure. Theorem: If R is a ring, then Q m a x r ( R ) {\displaystyle Q_{max}^{r}(R)}
K. S. S. Nambooripad (890 words) [view diff] exact match in snippet view article find links to article
sandwich matrices and wrote several expository papers on Nambooripad structure theorem for regular semigroups". He later developed an alternative approach
Krohn–Rhodes theory (2,310 words) [view diff] exact match in snippet view article find links to article
believed that the semigroup/monoid axioms were too weak to admit a structure theorem of any strength, and prior work (Hartmanis & Stearns) was only able
Wu's method of characteristic set (1,462 words) [view diff] exact match in snippet view article find links to article
geometries. J. Syst. Sci. Math. Sci., 4, 207–35 Wu, W. T. (1987). A zero structure theorem for polynomial equations solving. MM Research Preprints, 1, 2–12 Xiaoshan
Hopf algebra (4,397 words) [view diff] exact match in snippet view article find links to article
of the notion of Hopf algebra. Using this structure, Hopf proved a structure theorem for the cohomology algebra of Lie groups. Theorem (Hopf) Let A {\displaystyle
Cohen–Macaulay ring (3,123 words) [view diff] exact match in snippet view article find links to article
Cohen–Macaulay if and only if it is a hypersurface ring. There is also a structure theorem for Cohen–Macaulay rings of codimension 2, the Hilbert–Burch theorem:
Interpersonal ties (3,386 words) [view diff] case mismatch in snippet view article find links to article
by a signed graph. This effort led to an important and non-obvious Structure Theorem for signed graphs, which was published by Frank Harary in 1953. A
Dual Steenrod algebra (818 words) [view diff] exact match in snippet view article find links to article
structure maps for the dual Hopf algebra. It turns out there's a nice structure theorem for the dual Hopf algebra, separated by whether the prime is 2 {\displaystyle
Zariski's main theorem (1,601 words) [view diff] exact match in snippet view article find links to article
points that are isolated in their fiber is quasifinite over Y. Then structure theorem for quasi-finite morphisms applies and yields the desired result.
Lyapunov optimization (2,370 words) [view diff] no match in snippet view article find links to article
theorem for Markov chains. However, it does not require a Markov chain structure. Theorem (Lyapunov Drift). Suppose there are constants B ⩾ 0 , ε > 0 {\displaystyle
Direct integral (2,827 words) [view diff] exact match in snippet view article find links to article
the central decomposition theorem of von Neumann. In general, the structure theorem of Abelian von Neumann algebras represents Z(A) as an algebra of scalar
Structured program theorem (2,782 words) [view diff] case mismatch in snippet view article find links to article
writes that the more generic name was proposed by H.D. Mills as "The Structure Theorem" in the early 1970s.: 381  This version of the theorem replaces all
Persistent homology group (1,604 words) [view diff] exact match in snippet view article find links to article
given by the structure theorem of persistence homology. This multiset is known as the persistence barcode. Concretely, the structure theorem states that
Milnor K-theory (3,847 words) [view diff] exact match in snippet view article find links to article
) {\displaystyle K_{n}^{M}(F)} are divisible. There is a general structure theorem computing K n M ( F ( t ) ) {\displaystyle K_{n}^{M}(F(t))} for a
Homotopy associative algebra (4,777 words) [view diff] exact match in snippet view article find links to article
{\displaystyle m_{i}} are equal to 0 {\displaystyle 0} . Using the structure theorem for minimal models, there is a canonical A ∞ {\displaystyle A_{\infty
Bass–Serre theory (5,901 words) [view diff] exact match in snippet view article find links to article
j(gx) = g j(x) and j(ge) = g j(e). This result is also known as the structure theorem. One of the immediate consequences is the classic Kurosh subgroup
Congruence lattice problem (5,500 words) [view diff] exact match in snippet view article find links to article
pushed further?) The proof of the theorem above runs by setting a structure theorem for congruence lattices of semilattices—namely, the Erosion Lemma
Moy–Prasad filtration (4,086 words) [view diff] exact match in snippet view article find links to article
sequel to the paper defining their filtration, Moy and Prasad proved a structure theorem for depth-zero supercuspidal representations. Let x {\displaystyle
Descendant tree (group theory) (8,133 words) [view diff] no match in snippet view article
virtual periodicity, the latter techniques determine the quantitative structure. Theorem. For any infinite pro-p group S {\displaystyle S} of coclass r ≥ 1
Fields Medal (4,942 words) [view diff] exact match in snippet view article find links to article
of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite