Question

Is any Finitely generated module over an Artinian ring , Noetherian?

score 672 · Answer 1 · 2026-03-25 12:32:38

672

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Is any Finitely generated module over an Artinian ring , Noetherian?

Published on 25 Mar 2026 - 12:32

score 548 · Answer 2 · 2016-12-19 11:22:52

548

Views

Every non-zero noetherian module has a simple quotient module.

Published on 19 Dec 2016 - 11:22

score 404 · Answer 3 · 2026-03-25 15:49:53

404

Views

The dimension modulo a principal ideal in a Noetherian local ring

Published on 25 Mar 2026 - 15:49

score 211 · Answer 4 · 2017-01-08 09:53:06

211

Views

If every proper subring is noetherian then the ring is noetherian?

Published on 08 Jan 2017 - 9:53

score 278 · Answer 5 · 2026-03-25 12:31:59

278

Views

Noetherian, Artinian on graded ring and localization

Published on 25 Mar 2026 - 12:31

score 288 · Answer 6 · 2017-01-12 10:00:56

288

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Intersection of all symbolic powers of a prime ideal

Published on 12 Jan 2017 - 10:00

score 584 · Answer 7 · 2017-01-14 10:28:48

584

Views

Inverse image of a Noetherian module under a module morphism

Published on 14 Jan 2017 - 10:28

score 409 · Answer 8 · 2017-01-19 20:06:54

409

Views

What is an example of a Noetherian Semi-local ring with an infinite number of prime ideals?

Published on 19 Jan 2017 - 20:06

score 834 · Answer 9 · 2017-01-22 06:36:44

834

Views

If the localization of a ring at each prime ideal is Noetherian, does this imply that ring is Noetherian?

Published on 22 Jan 2017 - 6:36

score 321 · Answer 10 · 2017-01-24 03:54:19

321

Views

Summand Noetherian is Noetherian?

Published on 24 Jan 2017 - 3:54

score 178 · Answer 11 · 2026-03-25 02:59:17

178

Views

When does an integral group ring have finite global dimension?

Published on 25 Mar 2026 - 2:59

score 86 · Answer 12 · 2017-01-29 12:55:29

86

Views

Why $\ker \varphi|_N$ is finitely generated?

Published on 29 Jan 2017 - 12:55

score 283 · Answer 13 · 2017-01-30 19:35:26

283

Views

"De-localization" of a Noetherian module?

Published on 30 Jan 2017 - 19:35

score 118 · Answer 14 · 2026-03-25 12:34:36

118

Views

$M_p$ is artinian for all primes p, then M is artinian

Published on 25 Mar 2026 - 12:34

score 178 · Answer 15 · 2017-02-05 06:28:11

178

Views

Does radical ideals $\sqrt{I_1}\subseteq\sqrt{I_2}\cdots$ becoming stationary imply ideals $I_1\subseteq I_2\cdots$ becoming stationary?

Published on 05 Feb 2017 - 6:28

List Question

Is any Finitely generated module over an Artinian ring , Noetherian?

Every non-zero noetherian module has a simple quotient module.

The dimension modulo a principal ideal in a Noetherian local ring

If every proper subring is noetherian then the ring is noetherian?

Noetherian, Artinian on graded ring and localization

Intersection of all symbolic powers of a prime ideal

Inverse image of a Noetherian module under a module morphism

What is an example of a Noetherian Semi-local ring with an infinite number of prime ideals?

If the localization of a ring at each prime ideal is Noetherian, does this imply that ring is Noetherian?

Summand Noetherian is Noetherian?

When does an integral group ring have finite global dimension?

Why $\ker \varphi|_N$ is finitely generated?

"De-localization" of a Noetherian module?

$M_p$ is artinian for all primes p, then M is artinian

Does radical ideals $\sqrt{I_1}\subseteq\sqrt{I_2}\cdots$ becoming stationary imply ideals $I_1\subseteq I_2\cdots$ becoming stationary?

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