Question

let R be local Noetherian. Any finitely generated R-module N st. any short exact sequence with $N$-ending is exact after tensor with R-module is free

score 11 · Answer 1 · 2026-02-26 05:54:05

11

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let R be local Noetherian. Any finitely generated R-module N st. any short exact sequence with $N$-ending is exact after tensor with R-module is free

Published on 26 Feb 2026 - 5:54

score 15 · Answer 2 · 2026-03-04 17:50:56

15

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Let $A$ be a commutative local noetherian ring and let $I$ be a proper ideal of $A$. Prove that $\bigcap_{n=1}^\infty I^n = 0$.

Published on 04 Mar 2026 - 17:50

score 72 · Answer 3 · 2024-03-25 19:03:36

72

Views

When is the initial form of a principal ideal generated by the initial form of the original ideal's generator?

Published on 25 Mar 2024 - 19:03

score 106 · Answer 4 · 2026-03-25 11:06:56

106

Views

$H^i_I(M)$ is finitely generated iff the support of $Ext^{d-i}_S(M, S)$ has dimension zero

Published on 25 Mar 2026 - 11:06

score 60 · Answer 5 · 2015-02-10 08:49:48

60

Views

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

Published on 10 Feb 2015 - 8:49

score 5.3k · Answer 6 · 2015-02-11 12:14:10

5.3k

Views

The localization of a ring at a maximal ideal

Published on 11 Feb 2015 - 12:14

score 48 · Answer 7 · 2026-03-25 16:13:40

48

Views

is there a relationship between $\ell (R/I^n)$ and $\ell (R/I)$

Published on 25 Mar 2026 - 16:13

score 323 · Answer 8 · 2015-02-25 16:12:02

323

Views

Help with Atiyah-McDonald proof. $1 + \hat{m} = $ units $\implies A$ is a local ring.

Published on 25 Feb 2015 - 16:12

score 97 · Answer 9 · 2015-03-17 17:15:17

97

Views

Nontrivial map between finite modules over local noetherian ring

Published on 17 Mar 2015 - 17:15

score 304 · Answer 10 · 2015-07-15 07:07:58

304

Views

Flatness of $R/(x)$ with $R$ being local

Published on 15 Jul 2015 - 7:07

score 280 · Answer 11 · 2015-07-26 16:15:25

280

Views

"If $x$ is a non-unit, then $1-ux$ is a unit"

Published on 26 Jul 2015 - 16:15

score 1.6k · Answer 12 · 2015-09-15 05:28:32

1.6k

Views

If Tensor Product of Two Finitely Generated Modules Over a Local Ring is Zero then one of the Modules is Zero

Published on 15 Sep 2015 - 5:28

score 963 · Answer 13 · 2015-11-08 16:11:49

963

Views

Can a product of non-principal ideals be principal, in a local ring?

Published on 08 Nov 2015 - 16:11

score 727 · Answer 14 · 2026-03-20 12:54:37

727

Views

Local Ring with an another definition

Published on 20 Mar 2026 - 12:54

score 235 · Answer 15 · 2026-03-25 17:13:07

235

Views

About a short proof of Krull principal ideal theorem

Published on 25 Mar 2026 - 17:13

List Question

let R be local Noetherian. Any finitely generated R-module N st. any short exact sequence with $N$-ending is exact after tensor with R-module is free

Let $A$ be a commutative local noetherian ring and let $I$ be a proper ideal of $A$. Prove that $\bigcap_{n=1}^\infty I^n = 0$.

When is the initial form of a principal ideal generated by the initial form of the original ideal's generator?

$H^i_I(M)$ is finitely generated iff the support of $Ext^{d-i}_S(M, S)$ has dimension zero

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

The localization of a ring at a maximal ideal

is there a relationship between $\ell (R/I^n)$ and $\ell (R/I)$

Help with Atiyah-McDonald proof. $1 + \hat{m} = $ units $\implies A$ is a local ring.

Nontrivial map between finite modules over local noetherian ring

Flatness of $R/(x)$ with $R$ being local

"If $x$ is a non-unit, then $1-ux$ is a unit"

If Tensor Product of Two Finitely Generated Modules Over a Local Ring is Zero then one of the Modules is Zero

Can a product of non-principal ideals be principal, in a local ring?

Local Ring with an another definition

About a short proof of Krull principal ideal theorem

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