Find link

language:

Find link is a tool written by Edward Betts.

Longer titles found: Structure theorem for finitely generated modules over a principal ideal domain (view)

searching for Finitely generated module 18 found (76 total)

alternate case: finitely generated module

Faltings' annihilator theorem (244 words) [view diff] exact match in snippet view article find links to article

commutative ring theory), Faltings' annihilator theorem states: given a finitely generated module M over a Noetherian commutative ring A and ideals I, J, the following

Hilbert–Samuel function (925 words) [view diff] exact match in snippet view article find links to article

function, named after David Hilbert and Pierre Samuel, of a nonzero finitely generated module M {\displaystyle M} over a commutative Noetherian local ring A

Analytically unramified ring (557 words) [view diff] exact match in snippet view article find links to article

field of fractions K of R, the integral closure of S in K is a finitely generated module over S. The second follows from the first. Let K0 be a perfect

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

divisible by p). Height 2: the maximal ideal (p,T). The rank of a finitely generated module is the number of times the module Zp[[T]] occurs in it. This is

Stably free module (116 words) [view diff] exact match in snippet view article find links to article

stably free module is a module which is close to being free. A finitely generated module M over a ring R is stably free if there exist free finitely generated

Free module (1,809 words) [view diff] exact match in snippet view article find links to article

modules is generally not free (cf. the Baer–Specker group). A finitely generated module over a commutative local ring is free if and only if it is faithfully

Torsion-free module (591 words) [view diff] no match in snippet view article find links to article

isomorphic to an ideal of the ring. Over a Dedekind domain, a finitely-generated module is torsion-free if and only if it is projective, but is in general

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

holds. More generally, Theorem — Let R be a ring and M a nonzero finitely generated module over R . If x 1 , x 2 , … , x r {\displaystyle x_{1},x_{2},\dots

Essential extension (975 words) [view diff] no match in snippet view article find links to article

lemma is that J(R)M is a superfluous submodule of M when M is a finitely-generated module over R. This definition can be generalized to an arbitrary abelian

Completion of a ring (1,581 words) [view diff] exact match in snippet view article find links to article

Noetherian ring R is a flat module over R. The completion of a finitely generated module M over a Noetherian ring R can be obtained by extension of scalars:

Weyl algebra (1,519 words) [view diff] exact match in snippet view article find links to article

so the Weyl algebra has a very large center. In fact, it is a finitely generated module over its center; even more so, it is an Azumaya algebra over its

Affine monoid (1,113 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {Q} ^{n}} . Then P ∩ L {\displaystyle P\cap L} is a finitely generated module over the affine monoid C ∩ L {\displaystyle C\cap L} . (Theorem

Krull's principal ideal theorem (1,236 words) [view diff] exact match in snippet view article find links to article

{q}}^{(n)}/{\mathfrak {q}}^{(n+1)}} . Then, by Nakayama's lemma (which says a finitely generated module M is zero if M = I M {\displaystyle M=IM} for some ideal I contained

Bilinear form (2,700 words) [view diff] exact match in snippet view article find links to article

bilinear form is unimodular if V → V∗ is an isomorphism. Given a finitely generated module over a commutative ring, the pairing may be injective (hence "nondegenerate"

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

a subring of a commutative Noetherian ring B such that B is a finitely generated module over A, then A is a Noetherian ring. Similarly, if a ring A is

Ext functor (3,219 words) [view diff] exact match in snippet view article find links to article

}\operatorname {Ext} _{R}^{i}(M,N_{\alpha })\end{aligned}}} Let A be a finitely generated module over a commutative Noetherian ring R. Then Ext commutes with localization

Proj construction (3,567 words) [view diff] no match in snippet view article find links to article

x {\displaystyle O_{X,x}} then the degree-one elements form a finitely-generated module over O X , x {\displaystyle O_{X,x}} and also generate the stalk

List of inventions and discoveries by women (7,595 words) [view diff] exact match in snippet view article find links to article

algebraically independent elements y1, y2, ..., yd in A such that A is a finitely generated module over the polynomial ring S:=k[y1, y2, ..., yd]. The theorem has