Question

$\mathfrak{m}^k$ is maximal if $\mathfrak{m}$ is

score 29 · Answer 1 · 2026-03-25 11:01:01

29

Views

$\mathfrak{m}^k$ is maximal if $\mathfrak{m}$ is

Published on 25 Mar 2026 - 11:01

score 428 · Answer 2 · 2026-05-10 17:27:10

428

Views

PIDs are not Artinian?

Published on 10 May 2026 - 17:27

score 53 · Answer 3 · 2026-03-25 11:04:53

53

Views

If $R$ is a commutative Artinian ring and $a\in R$, is $A_M:=\{f_a\mid f_a:M\to M,m\mapsto ma\}$ an Artinian ring?

Published on 25 Mar 2026 - 11:04

score 293 · Answer 4 · 2026-03-25 11:06:29

293

Views

$A,B$ Noetherian rings, $A\subseteq B$ integral extension, $\mathfrak m $ a maximal ideal of $A \implies B/\mathfrak m B$ is Artinian

Published on 25 Mar 2026 - 11:06

score 395 · Answer 5 · 2026-04-15 22:04:02

395

Views

In a local ring, the maximal ideal $\mathfrak{m}$ is principal $\implies \dim_k(\mathfrak{m}/\mathfrak{m}^2)\leq 1$

Published on 15 Apr 2026 - 22:04

score 463 · Answer 6 · 2026-04-14 04:54:43

463

Views

$R$ be an infinite commutative ring such that $R/I$ has only finitely many ideals for every non-zero ideal $I$ , what can we say about $R$?

Published on 14 Apr 2026 - 4:54

score 140 · Answer 7 · 2026-04-12 01:59:22

140

Views

$C$ be a subring of $B$ which is again a subring of $A$ , let $A,B,C$ be Noetherian and $A \cong C$ , then is $A \cong B$?

Published on 12 Apr 2026 - 1:59

score 638 · Answer 8 · 2026-04-08 16:58:21

638

Views

About Fitting decomposition theorem of module

Published on 08 Apr 2026 - 16:58

score 534 · Answer 9 · 2026-04-10 19:26:03

534

Views

Techniques for Proving a Ring is Artinian?

Published on 10 Apr 2026 - 19:26

score 222 · Answer 10 · 2026-04-12 06:51:14

222

Views

An elementary proof that artinian modules over left-artinian rings finitely generated?

Published on 12 Apr 2026 - 6:51

score 2k · Answer 11 · 2026-04-15 04:39:57

2k

Views

For $k$ a field, $k[x]$ is Noetherian but not Artinian?

Published on 15 Apr 2026 - 4:39

score 222 · Answer 12 · 2026-04-12 18:56:59

222

Views

Is $\oplus_{\mathbb{N}}\mathbb{Z}_2$ Artinian but not Noetherian?

Published on 12 Apr 2026 - 18:56

score 439 · Answer 13 · 2026-04-09 19:49:54

439

Views

Structure theorem for commutative Noetherian rings

Published on 09 Apr 2026 - 19:49

score 2k · Answer 14 · 2026-04-14 02:36:24

2k

Views

Characterising subgroups of Prüfer $p$-groups.

Published on 14 Apr 2026 - 2:36

score 692 · Answer 15 · 2026-04-16 12:53:37

692

Views

Over an artinian ring every nonzero module has a simple submodule?

Published on 16 Apr 2026 - 12:53

List Question

$\mathfrak{m}^k$ is maximal if $\mathfrak{m}$ is

PIDs are not Artinian?

If $R$ is a commutative Artinian ring and $a\in R$, is $A_M:=\{f_a\mid f_a:M\to M,m\mapsto ma\}$ an Artinian ring?

$A,B$ Noetherian rings, $A\subseteq B$ integral extension, $\mathfrak m $ a maximal ideal of $A \implies B/\mathfrak m B$ is Artinian

In a local ring, the maximal ideal $\mathfrak{m}$ is principal $\implies \dim_k(\mathfrak{m}/\mathfrak{m}^2)\leq 1$

$R$ be an infinite commutative ring such that $R/I$ has only finitely many ideals for every non-zero ideal $I$ , what can we say about $R$?

$C$ be a subring of $B$ which is again a subring of $A$ , let $A,B,C$ be Noetherian and $A \cong C$ , then is $A \cong B$?

About Fitting decomposition theorem of module

Techniques for Proving a Ring is Artinian?

An elementary proof that artinian modules over left-artinian rings finitely generated?

For $k$ a field, $k[x]$ is Noetherian but not Artinian?

Is $\oplus_{\mathbb{N}}\mathbb{Z}_2$ Artinian but not Noetherian?

Structure theorem for commutative Noetherian rings

Characterising subgroups of Prüfer $p$-groups.

Over an artinian ring every nonzero module has a simple submodule?

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