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11 votes
1 answer
2k views

geometric interpretation and differences of Gorenstein rings, Complete intersections and regular rings

7 votes
2 answers
696 views

invariants that can be measured by Local Cohomology

6 votes
1 answer
271 views

local UFD with dimension less than or equal 3 is catenary

6 votes
1 answer
345 views

Assuming $\operatorname{depth}M\ge \operatorname{depth}N$, what can one say about $\operatorname{depth}M_p$ and $\operatorname{depth}N_p$?

5 votes
0 answers
94 views

How far finiteness dimension can be from edges? Example for $f_m(S/I)\ge depth S/I+2$

4 votes
3 answers
600 views

canonical module can be identified with an ideal. how can one reach that ideal?

3 votes
0 answers
114 views

intersection of two height 2 primes must contain a non-zero prime?

3 votes
1 answer
258 views

relate shellability of a simplicial complex to the links of its faces

3 votes
1 answer
274 views

Let $f:R\to S$ be a local finite monomorphism .If $M$ is an Artinian $S$-module, is it an Artinian $R$-module?

3 votes
2 answers
535 views

How a "sequentially Cohen–Macaulay" simplicial complex relates to "Cohen–Macaulay" simplicial complex?

3 votes
1 answer
228 views

Localization of the pullback diagram

3 votes
3 answers
283 views

Examples of integral ring extensions that $\operatorname{ht}P \lt \operatorname{ht}P\cap A$

2 votes
1 answer
282 views

Property of a commutative ring that is determined by the prime ideals of the ring

2 votes
0 answers
81 views

Let $R$ be a non-catenary, and $f: R \to S$ be a finite monomorphism. Can $S$ be catenary?

2 votes
1 answer
105 views

Is there a characterization of r(M) by local cohomology instead of Ext

2 votes
1 answer
207 views

when there is an injection $0 \to R \to K_R$?

2 votes
1 answer
1k views

In what conditions every ideal is an extension ideal? Is every prime ideal extension of prime ideal?

2 votes
1 answer
241 views

$Hom (T,R)$ isomorphic to $R:T$?

2 votes
2 answers
241 views

if $R$ is Noetherian local with a finite module of finite injective dimension and if "?" , then $R$ is "Gorenstein"

2 votes
1 answer
238 views

Does the going-up theorem hold between flat algebras?

2 votes
1 answer
750 views

intuitive interpretation of analytic spread

2 votes
1 answer
284 views

finiteness dimension

2 votes
2 answers
103 views

Does $fd(M)\lt \infty$ and $id(M)\lt \infty $ imply that $R$ is Gorenstein?

1 vote
1 answer
345 views

Graded version of Baer's Criterion

1 vote
1 answer
198 views

betti-numbers of Gin(I), generic initial ideal of $I$

1 vote
1 answer
149 views

$IM=mM$. can we say that $I$ is a reduction ideal of $m$?

1 vote
1 answer
214 views

M is an R-module which is not finitely generated. is it true that $\inf \{ i| H^i_I(M)\neq 0 \}\le ht_M I?$

1 vote
0 answers
84 views

if $\Delta$ is pure, then what happens to betti-numbers of $I_{\Delta}$ or $I_{\Delta^v}$

1 vote
1 answer
127 views

Theorem 16 , Chapter 5 of Northcott 's, Finite Free Resolutions: p.grade

1 vote
0 answers
392 views

Source for conjectures in commutative algebra