Question

$M$ is artinian or noetherian $\implies$ M has a composition series.

score 555 · Answer 1 · 2017-04-04 21:34:02

555

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$M$ is artinian or noetherian $\implies$ M has a composition series.

Published on 04 Apr 2017 - 21:34

score 427 · Answer 2 · 2026-03-25 06:06:59

427

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$R$ is a prime right Goldie ring which contains a minimal right ideal. Show that $R$ must be a simple Artinian ring.

Published on 25 Mar 2026 - 6:06

score 116 · Answer 3 · 2023-02-14 07:31:39

116

Views

Let $A\subseteq B$ be a finite ring extension. Let $M$ be a Noetherian/Artinian $B$-module. Show $M$ is a Noetherian/Artinian $A$-module.

Published on 14 Feb 2023 - 7:31

score 58 · Answer 4 · 2023-02-21 15:08:17

58

Views

In Lemma 10.53.5 of Stacks (about commutative Artinian rings), how did they use localisation?

Published on 21 Feb 2023 - 15:08

score 77 · Answer 5 · 2023-03-15 18:21:23

77

Views

If $A$ is Noetherian ring with ideal $I$, then $I$-adic completion ${\hat{A}}$ is Noetherian

Published on 15 Mar 2023 - 18:21

score 50 · Answer 6 · 2023-03-17 17:22:46

50

Views

Indecomposability of a factor of two indecomposable modules

Published on 17 Mar 2023 - 17:22

score 112 · Answer 7 · 2023-03-20 08:07:33

112

Views

Ideal of definition of local ring

Published on 20 Mar 2023 - 8:07

score 43 · Answer 8 · 2023-08-20 09:19:29

43

Views

Is the projective direct summand of middle of an exact sequence is determined by others?

Published on 20 Aug 2023 - 9:19

score 67 · Answer 9 · 2023-08-22 11:57:11

67

Views

Quotient of infinite product of fields which is semi-artinian

Published on 22 Aug 2023 - 11:57

score 42 · Answer 10 · 2026-02-23 05:40:37

42

Views

stable range of stably free modules

Published on 23 Feb 2026 - 5:40

score 29 · Answer 11 · 2023-09-15 16:30:10

29

Views

$Spec(R)$ finite and discrete implies $R_{red}$ Artinian proof verification

Published on 15 Sep 2023 - 16:30

score 42 · Answer 12 · 2023-09-21 12:33:42

42

Views

Example of absolutely flat semi-artinian ring

Published on 21 Sep 2023 - 12:33

score 73 · Answer 13 · 2023-10-25 02:19:34

73

Views

Embedding of modules of finite length

Published on 25 Oct 2023 - 2:19

score 19 · Answer 14 · 2023-10-27 05:59:59

19

Views

counter-example for quotient of artinian and noetherian modules

Published on 27 Oct 2023 - 5:59

score 58 · Answer 15 · 2023-10-30 22:26:43

58

Views

possibility of $\mathbb{Q}[x]$ being artinian as a quotient

Published on 30 Oct 2023 - 22:26

List Question

$M$ is artinian or noetherian $\implies$ M has a composition series.

$R$ is a prime right Goldie ring which contains a minimal right ideal. Show that $R$ must be a simple Artinian ring.

Let $A\subseteq B$ be a finite ring extension. Let $M$ be a Noetherian/Artinian $B$-module. Show $M$ is a Noetherian/Artinian $A$-module.

In Lemma 10.53.5 of Stacks (about commutative Artinian rings), how did they use localisation?

If $A$ is Noetherian ring with ideal $I$, then $I$-adic completion ${\hat{A}}$ is Noetherian

Indecomposability of a factor of two indecomposable modules

Ideal of definition of local ring

Is the projective direct summand of middle of an exact sequence is determined by others?

Quotient of infinite product of fields which is semi-artinian

stable range of stably free modules

$Spec(R)$ finite and discrete implies $R_{red}$ Artinian proof verification

Example of absolutely flat semi-artinian ring

Embedding of modules of finite length

counter-example for quotient of artinian and noetherian modules

possibility of $\mathbb{Q}[x]$ being artinian as a quotient

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