Question

Noetherian/Artinian modules

score 179 · Answer 1 · 2026-03-25 12:30:04

179

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Noetherian/Artinian modules

Published on 25 Mar 2026 - 12:30

score 174 · Answer 2 · 2017-02-23 22:05:48

174

Views

$\mathcal{O}/(\mathcal{O}\cap I\mathcal{O}_P)\cong \mathcal{O}_P/I\mathcal{O}_p$ if $\mathcal{O}$ is a noetherian one dimensional domain.

Published on 23 Feb 2017 - 22:05

score 487 · Answer 3 · 2026-03-25 12:30:31

487

Views

Artinian ring is Noetherian

Published on 25 Mar 2026 - 12:30

score 131 · Answer 4 · 2017-02-26 11:52:28

131

Views

An exercise about Laskerian module in Bourbaki (commutative algebra)

Published on 26 Feb 2017 - 11:52

score 6.7k · Answer 5 · 2017-02-26 23:02:17

6.7k

Views

Ideals of ring finitely generated if and only if ring Noetherian

Published on 26 Feb 2017 - 23:02

score 1.2k · Answer 6 · 2026-03-25 12:30:37

1.2k

Views

Difference between Artinian and Noetherian rings

Published on 25 Mar 2026 - 12:30

score 320 · Answer 7 · 2017-03-08 19:04:40

320

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Let $R$ be a right noetherian ring. Then every injective envelope is a direct sum of indecomposable modules.

Published on 08 Mar 2017 - 19:04

score 856 · Answer 8 · 2017-03-16 16:52:25

856

Views

Are all the subrings of $\mathbb Q$ noetherians?

Published on 16 Mar 2017 - 16:52

score 595 · Answer 9 · 2017-03-19 02:50:50

595

Views

Help verifying an example of ascending chain condition.

Published on 19 Mar 2017 - 2:50

score 607 · Answer 10 · 2017-03-27 04:35:09

607

Views

Do Noetherian rings have the IBN property?

Published on 27 Mar 2017 - 4:35

score 556 · Answer 11 · 2026-03-25 14:04:17

556

Views

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

Published on 25 Mar 2026 - 14:04

score 46 · Answer 12 · 2026-03-25 06:04:12

46

Views

General method of finding dimension of a ring and determining regularity

Published on 25 Mar 2026 - 6:04

score 117 · Answer 13 · 2026-03-25 14:07:01

117

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 25 Mar 2026 - 14:07

score 118 · Answer 14 · 2023-02-15 10:33:40

118

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Example of an Artinian $B$-Module $M$ and a finite extension $A\subseteq B$ such that $M$ isn't $A$-Artinian

Published on 15 Feb 2023 - 10:33

score 104 · Answer 15 · 2023-02-21 14:11:28

104

Views

If $R$ is a right Noetherian ring, then so is $eRe$ for every idempotent $e\in R$.

Published on 21 Feb 2023 - 14:11

List Question

Noetherian/Artinian modules

$\mathcal{O}/(\mathcal{O}\cap I\mathcal{O}_P)\cong \mathcal{O}_P/I\mathcal{O}_p$ if $\mathcal{O}$ is a noetherian one dimensional domain.

Artinian ring is Noetherian

An exercise about Laskerian module in Bourbaki (commutative algebra)

Ideals of ring finitely generated if and only if ring Noetherian

Difference between Artinian and Noetherian rings

Let $R$ be a right noetherian ring. Then every injective envelope is a direct sum of indecomposable modules.

Are all the subrings of $\mathbb Q$ noetherians?

Help verifying an example of ascending chain condition.

Do Noetherian rings have the IBN property?

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

General method of finding dimension of a ring and determining regularity

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.

Example of an Artinian $B$-Module $M$ and a finite extension $A\subseteq B$ such that $M$ isn't $A$-Artinian

If $R$ is a right Noetherian ring, then so is $eRe$ for every idempotent $e\in R$.

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