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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

3 votes
0 answers
129 views

What is the $Ass(Ext^p_R(M,R))$?

Let $R$ be a Noetherian commutative local ring, $M$ a finitely generated $R$-module with $p=pd M<\infty$ (projective dimension of $M$). What is the relation between $Ass(Ext^p_R(M,R))$ and $Ass(M)$? T …
1 vote
1 answer
209 views

On Krull dimension \dim M and \dim Supp(M)

Let $R$ be a commutative Noetherian ring and $M$ an $R$-module (not finitely generated). Are $\dim M$ and $\dim Supp(M)$ same?
0 votes
1 answer
109 views

$0 :_M I^n$ is finitely generated for all $i\ge 1$?

I see the remark that: "Let $R$ be a Noetherian commutative ring, $M$ an $R$-module and $I$ an ideal of $R.$ Assume that $0 :_M I$ is finitely generated. Then $0 :_M I^n$ is finitely generated for all …