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searching for Noetherian ring 16 found (140 total)

Concha Gómez (509 words) [view diff] case mismatch in snippet view article find links to article

known for being one of the co-founders of the women's organization The Noetherian Ring at the University of California Berkeley in 1991 while attending as

Tight closure (469 words) [view diff] exact match in snippet view article find links to article

Craig Huneke (1988, 1990). Let R {\displaystyle R} be a commutative noetherian ring containing a field of characteristic p > 0 {\displaystyle p>0} . Hence

Stable range condition (548 words) [view diff] exact match in snippet view article find links to article

also generate the unit ideal. If R {\displaystyle R} is a commutative Noetherian ring of Krull dimension d {\displaystyle d} , then the stable range of R

Ideal reduction (420 words) [view diff] exact match in snippet view article find links to article

minimal prime ideals over them (the converse is false). If R is a Noetherian ring, then J is a reduction of I if and only if the Rees algebra R[It] is

Coherent sheaf (6,934 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X=\operatorname {Spec} (R)} , R {\displaystyle R} a Noetherian ring. Then vector bundles on X {\displaystyle X} are exactly the sheaves

Principal ideal (1,332 words) [view diff] exact match in snippet view article find links to article

Krull's principal ideal theorem states that if R {\displaystyle R} is a Noetherian ring and I {\displaystyle I} is a principal, proper ideal of R , {\displaystyle

Ideal (ring theory) (6,347 words) [view diff] exact match in snippet view article

generated by a system of parameters. Perfect ideal: A proper ideal I in a Noetherian ring R {\displaystyle R} is called a perfect ideal if its grade equals the

Bianca Viray (509 words) [view diff] case mismatch in snippet view article find links to article

her work on Girl’s Angle, the Women In Numbers research network, the Noetherian Ring, the Western Algebraic Geometry Symposium, and for launching new and

Formal scheme (1,031 words) [view diff] exact match in snippet view article find links to article

isomorphic (as topologically ringed spaces) to the formal spectrum of a noetherian ring. A morphism f : X → Y {\displaystyle f:{\mathfrak {X}}\to {\mathfrak

Gordan's lemma (1,251 words) [view diff] exact match in snippet view article find links to article

Let A be a Z {\displaystyle \mathbb {Z} } -graded ring. If A is a Noetherian ring, then A + = ⊕ 0 ∞ A n {\displaystyle A^{+}=\oplus _{0}^{\infty }A_{n}}

Coherent duality (1,897 words) [view diff] exact match in snippet view article find links to article

proved by Yekutieli and Zhang assuming k {\displaystyle k} is a regular noetherian ring of finite Krull dimension, and by Avramov, Iyengar and Lipman assuming

Projective variety (7,499 words) [view diff] exact match in snippet view article find links to article

Let X be a projective scheme over a field (or, more generally over a Noetherian ring A). Cohomology of coherent sheaves F {\displaystyle {\mathcal {F}}}

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

formulation as follows: If B is an algebra of finite type over a local Noetherian ring A, and n is a maximal ideal of B which is minimal among ideals of B

Sheaf of modules (3,459 words) [view diff] exact match in snippet view article find links to article

Hartshorne, drop the subscript O. Assume X is a projective scheme over a Noetherian ring. Let F, G be coherent sheaves on X and i an integer. Then there exists

Divisor (algebraic geometry) (6,609 words) [view diff] exact match in snippet view article

reduced Noetherian schemes, or for quasi-projective schemes over a Noetherian ring, but it can fail in general (even for proper schemes over C), which

Koszul complex (5,528 words) [view diff] exact match in snippet view article find links to article

characterization of a depth. Theorem (depth-sensitivity) — Let R be a Noetherian ring, x1, ..., xn elements of R and I = (x1, ..., xn) the ideal generated