Question

If $M$ is finitely generated left module over a left noetherian ring $R$, then $M$ is a noetherian module.

score 1k · Answer 1 · 2017-06-20 09:52:02

1k

Views

If $M$ is finitely generated left module over a left noetherian ring $R$, then $M$ is a noetherian module.

Published on 20 Jun 2017 - 9:52

score 823 · Answer 2 · 2026-03-25 18:46:30

823

Views

Are noetherian modules over noetherian ring and artinian modules over artinian ring finitely generated?

Published on 25 Mar 2026 - 18:46

score 176 · Answer 3 · 2017-06-22 23:17:45

176

Views

Is $R\langle x_1,\ldots,x_n\rangle$ Noetherian?

Published on 22 Jun 2017 - 23:17

score 166 · Answer 4 · 2026-03-28 10:16:40

166

Views

Integral domains $R$ such that any ring $R \subset S \subset K$ is Noetherian

Published on 28 Mar 2026 - 10:16

score 187 · Answer 5 · 2017-06-29 22:22:43

187

Views

In a Noetherian domain $R$, if $I\neq R$ then $\bigcap_{n=1}^\infty I^n=0$?

Published on 29 Jun 2017 - 22:22

score 272 · Answer 6 · 2026-03-26 02:47:51

272

Views

What is an example of a noetherian local integral domain $R$ of Krull dimension 1?

Published on 26 Mar 2026 - 2:47

score 433 · Answer 7 · 2017-07-11 17:23:08

433

Views

Basis of the localization of module

Published on 11 Jul 2017 - 17:23

score 74 · Answer 8 · 2026-03-27 12:30:17

74

Views

$R$ right Noetherian. Is it true that $R(x)\otimes_{R[x]}R(x)\cong R(x)$?

Published on 27 Mar 2026 - 12:30

score 690 · Answer 9 · 2026-02-23 13:05:54

690

Views

Showing tensor product of f.g. reduced $k$-algebras is reduced where I should assume $k$ algebraically closed?

Published on 23 Feb 2026 - 13:05

score 340 · Answer 10 · 2017-08-08 07:49:40

340

Views

Does the strong form of Hilbert Nullstellensatz say how the maximal ideals look like?

Published on 08 Aug 2017 - 7:49

score 285 · Answer 11 · 2026-03-26 14:25:22

285

Views

A question regarding isomorphism of group rings

Published on 26 Mar 2026 - 14:25

score 1.5k · Answer 12 · 2017-08-22 12:49:00

1.5k

Views

If every prime ideal in a ring $R$ is finitely generated, then $R$ is Noetherian?

Published on 22 Aug 2017 - 12:49

score 140 · Answer 13 · 2017-08-24 05:51:13

140

Views

If $R_{\mathfrak{p}}$ is an integral domain then $R_f$ is also an integral domain for some $f\notin \mathfrak{p}$

Published on 24 Aug 2017 - 5:51

score 298 · Answer 14 · 2026-03-25 18:47:32

298

Views

Special kind of commutative semi-local ring

Published on 25 Mar 2026 - 18:47

score 212 · Answer 15 · 2017-09-01 10:34:59

212

Views

Necessary and sufficient conditions for Noetherian integral domain to be integrally closed

Published on 01 Sep 2017 - 10:34

List Question

If $M$ is finitely generated left module over a left noetherian ring $R$, then $M$ is a noetherian module.

Are noetherian modules over noetherian ring and artinian modules over artinian ring finitely generated?

Is $R\langle x_1,\ldots,x_n\rangle$ Noetherian?

Integral domains $R$ such that any ring $R \subset S \subset K$ is Noetherian

In a Noetherian domain $R$, if $I\neq R$ then $\bigcap_{n=1}^\infty I^n=0$?

What is an example of a noetherian local integral domain $R$ of Krull dimension 1?

Basis of the localization of module

$R$ right Noetherian. Is it true that $R(x)\otimes_{R[x]}R(x)\cong R(x)$?

Showing tensor product of f.g. reduced $k$-algebras is reduced where I should assume $k$ algebraically closed?

Does the strong form of Hilbert Nullstellensatz say how the maximal ideals look like?

A question regarding isomorphism of group rings

If every prime ideal in a ring $R$ is finitely generated, then $R$ is Noetherian?

If $R_{\mathfrak{p}}$ is an integral domain then $R_f$ is also an integral domain for some $f\notin \mathfrak{p}$

Special kind of commutative semi-local ring

Necessary and sufficient conditions for Noetherian integral domain to be integrally closed

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