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

2 votes
1 answer
183 views

An example of a local ring which is not CM and a MCM module over it

I am looking for an example of a commutative noetherian local ring $(A,m)$, and a maximal Cohen-Macaulay module $M$ over $A$ (in particular $M$ is finitely generated over $A$), such that for some $p \ …
4 votes
0 answers
83 views

Support of Matlis dual

Let $(A,m)$ be a commutative noetherian local ring, $E$ the injective hull of $A/m$, and $M$ a finitely generated $A$-module. What is the connection between the support of $M$ and the support of the …
4 votes
0 answers
204 views

Dimension of a fiber of a local homomorphism

Let $\varphi:(R,m) \to (S,n)$ be a local homomorphism between local noetherian rings. Recall that the fiber of $\varphi$ is by definition the ring $F(\varphi) = S/mS$. If $\varphi$ is flat, it is we …