Question

For which Noetherian local rings, is every associated prime ideal contained in the square of the maximal ideal?

score 213 · Answer 1 · 2026-03-25 19:06:50

213

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For which Noetherian local rings, is every associated prime ideal contained in the square of the maximal ideal?

Published on 25 Mar 2026 - 19:06

score 663 · Answer 2 · 2026-03-28 21:34:12

663

Views

Let $A$ be a valuation ring of a field $K$. Show that every subring of $K$ which contains $A$ is a local ring of $A$.

Published on 28 Mar 2026 - 21:34

score 117 · Answer 3 · 2026-03-25 13:56:24

117

Views

Is $\widehat{IM}=\widehat I \widehat M$ for any finitely generated module $M$, where $\widehat {(-)}$ denotes completion w.r.t. maximal ideal?

Published on 25 Mar 2026 - 13:56

score 167 · Answer 4 · 2021-07-30 11:09:35

167

Views

ring of formal power series is not always local ring?

Published on 30 Jul 2021 - 11:09

score 120 · Answer 5 · 2021-08-10 22:06:26

120

Views

Let $A$ be an integrally closed noetherian domain, and $(R, \mathfrak{m})$ local with $A \subseteq R \subseteq K(A)$. Is $R$ a localization of $A$?

Published on 10 Aug 2021 - 22:06

score 37 · Answer 6 · 2026-03-25 23:20:46

37

Views

Hypothesis - am I doing this right? (Local, principal ideal ring)

Published on 25 Mar 2026 - 23:20

score 187 · Answer 7 · 2021-08-18 22:35:38

187

Views

Is a local ring with a certain finite quotient necessarily noetherian?

Published on 18 Aug 2021 - 22:35

score 202 · Answer 8 · 2021-08-20 04:34:14

202

Views

For a Noetherian local ring of positive depth, the maximal ideal can be generated by non-zero-divisors?

Published on 20 Aug 2021 - 4:34

score 220 · Answer 9 · 2026-03-26 03:01:25

220

Views

Maximal Cohen-Macaulay modules of full support, over non-artinian local Cohen-Macaulay rings, are faithful?

Published on 26 Mar 2026 - 3:01

score 237 · Answer 10 · 2026-03-25 15:43:43

237

Views

derivations of the ring of germs of $C^{\infty}$ functions

Published on 25 Mar 2026 - 15:43

score 217 · Answer 11 · 2021-09-06 02:19:01

217

Views

Noetherian local ring of depth $1$ whose localization at some prime ideal has higher depth?

Published on 06 Sep 2021 - 2:19

score 111 · Answer 12 · 2021-09-06 20:54:25

111

Views

surjection of complete noetherian local rings -reference help

Published on 06 Sep 2021 - 20:54

score 35 · Answer 13 · 2021-09-09 13:46:26

35

Views

A basic question on commutative finite local rings

Published on 09 Sep 2021 - 13:46

score 269 · Answer 14 · 2021-09-10 00:03:58

269

Views

Questions regarding solution to showing: $M\otimes_A N = 0 \implies M = 0$ or $N = 0$.

Published on 10 Sep 2021 - 0:03

score 103 · Answer 15 · 2021-09-15 11:05:19

103

Views

Question about socle in Huneke, Sega and Vraciu's paper.

Published on 15 Sep 2021 - 11:05

List Question

For which Noetherian local rings, is every associated prime ideal contained in the square of the maximal ideal?

Let $A$ be a valuation ring of a field $K$. Show that every subring of $K$ which contains $A$ is a local ring of $A$.

Is $\widehat{IM}=\widehat I \widehat M$ for any finitely generated module $M$, where $\widehat {(-)}$ denotes completion w.r.t. maximal ideal?

ring of formal power series is not always local ring?

Let $A$ be an integrally closed noetherian domain, and $(R, \mathfrak{m})$ local with $A \subseteq R \subseteq K(A)$. Is $R$ a localization of $A$?

Hypothesis - am I doing this right? (Local, principal ideal ring)

Is a local ring with a certain finite quotient necessarily noetherian?

For a Noetherian local ring of positive depth, the maximal ideal can be generated by non-zero-divisors?

Maximal Cohen-Macaulay modules of full support, over non-artinian local Cohen-Macaulay rings, are faithful?

derivations of the ring of germs of $C^{\infty}$ functions

Noetherian local ring of depth $1$ whose localization at some prime ideal has higher depth?

surjection of complete noetherian local rings -reference help

A basic question on commutative finite local rings

Questions regarding solution to showing: $M\otimes_A N = 0 \implies M = 0$ or $N = 0$.

Question about socle in Huneke, Sega and Vraciu's paper.

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