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Results tagged with ac.commutative-algebra
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user 479623
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Cohomological dimension and height of ideals
Let $I$ be an ideal in a Noetherian ring $R$. We define the cohomological dimension of $I$ to be $\operatorname{cd}(I)=\operatorname{sup}\{i\in \mathbb N:\operatorname{H}_I^i(R)\neq0\}$ and it is know …
- 33
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Quotient Cohen-Macaulay ring and associated primes
Does there exist such (local) Cohen-Macaulay Noetherian ring $(R,m)$ with some $p\in \operatorname{Ass}R$ so that $R/p$ is not Cohen-Macaulay? (I am especially curious about the case where $R$ is a Co …
- 5,429