Question

Is a commutative perfect and coherent ring an Artin ring?

score 67 · Answer 1 · 2026-03-25 05:59:43

67

Views

Is a commutative perfect and coherent ring an Artin ring?

Published on 25 Mar 2026 - 5:59

score 34 · Answer 2 · 2023-12-03 16:59:24

34

Views

Idempotents in centralizers of non-nilpotent zero divisors

Published on 03 Dec 2023 - 16:59

score 49 · Answer 3 · 2023-12-20 03:59:06

49

Views

If an Artinian module $M$ is a sum of submodules of length $\le n$, then it is also of finite length

Published on 20 Dec 2023 - 3:59

score 108 · Answer 4 · 2024-01-03 11:39:01

108

Views

A case where submodules, isomorphic as modules, are isomorphic as submodules

Published on 03 Jan 2024 - 11:39

score 51 · Answer 5 · 2024-01-05 13:52:03

51

Views

If the start and end of an exact sequence are both Artinian modules, then is the middle one also an Artinian module?

Published on 05 Jan 2024 - 13:52

score 86 · Answer 6 · 2024-03-23 15:46:56

86

Views

Checking if a ring is Artinian.

Published on 23 Mar 2024 - 15:46

score 2.3k · Answer 7 · 2026-02-23 07:45:18

2.3k

Views

$R$ is semisimple iff it is Artinian and $J(R) = 0$

Published on 23 Feb 2026 - 7:45

score 1k · Answer 8 · 2026-02-23 07:46:25

1k

Views

Prove that $M$ is finitely generated and semisimple, if Artinian and the intersection of all maximal submodules is zero

Published on 23 Feb 2026 - 7:46

score 240 · Answer 9 · 2016-03-22 16:27:55

240

Views

Nilpotent or just nil idempotent ideal?

Published on 22 Mar 2016 - 16:27

score 621 · Answer 10 · 2016-04-04 06:41:54

621

Views

Example of a non noetherian module $M$ s.t. $M/IM$ is noetherian

Published on 04 Apr 2016 - 6:41

score 376 · Answer 11 · 2016-04-04 07:14:02

376

Views

Let $R$ be a ring and $I$ be a finitely generated nilpotent ideal. If $R/I$ is noetherian (resp. Artinian) then $R$ is so.

Published on 04 Apr 2016 - 7:14

score 492 · Answer 12 · 2016-04-09 08:18:52

492

Views

Proof of commutative Artinian ring is Noetherian

Published on 09 Apr 2016 - 8:18

score 57 · Answer 13 · 2016-04-24 13:00:53

57

Views

Can we find ( characterize ) all non-zero commutative Artinian rings $R$ for which $-1 , 1$ are the only units of $R$ ?

Published on 24 Apr 2016 - 13:00

score 288 · Answer 14 · 2016-04-25 03:13:21

288

Views

Artinian - Noetherian rings and modules suggest study guide

Published on 25 Apr 2016 - 3:13

score 113 · Answer 15 · 2026-03-06 06:28:04

113

Views

Dimension of an Artin $K$-algebra and cardinal of its spectrum

Published on 06 Mar 2026 - 6:28

List Question

Is a commutative perfect and coherent ring an Artin ring?

Idempotents in centralizers of non-nilpotent zero divisors

If an Artinian module $M$ is a sum of submodules of length $\le n$, then it is also of finite length

A case where submodules, isomorphic as modules, are isomorphic as submodules

If the start and end of an exact sequence are both Artinian modules, then is the middle one also an Artinian module?

Checking if a ring is Artinian.

$R$ is semisimple iff it is Artinian and $J(R) = 0$

Prove that $M$ is finitely generated and semisimple, if Artinian and the intersection of all maximal submodules is zero

Nilpotent or just nil idempotent ideal?

Example of a non noetherian module $M$ s.t. $M/IM$ is noetherian

Let $R$ be a ring and $I$ be a finitely generated nilpotent ideal. If $R/I$ is noetherian (resp. Artinian) then $R$ is so.

Proof of commutative Artinian ring is Noetherian

Can we find ( characterize ) all non-zero commutative Artinian rings $R$ for which $-1 , 1$ are the only units of $R$ ?

Artinian - Noetherian rings and modules suggest study guide

Dimension of an Artin $K$-algebra and cardinal of its spectrum

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