Question

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

score 28 · Answer 1 · 2020-07-01 09:42:59

28

Views

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

Published on 01 Jul 2020 - 9:42

score 425 · Answer 2 · 2020-07-05 07:38:33

425

Views

PIDs are not Artinian?

Published on 05 Jul 2020 - 7:38

score 52 · Answer 3 · 2020-07-24 13:16:46

52

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 24 Jul 2020 - 13:16

score 292 · Answer 4 · 2020-07-29 16:11:50

292

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 29 Jul 2020 - 16:11

score 392 · Answer 5 · 2016-07-10 14:07:43

392

Views

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

Published on 10 Jul 2016 - 14:07

score 460 · Answer 6 · 2016-07-27 05:28:28

460

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 27 Jul 2016 - 5:28

score 137 · Answer 7 · 2016-08-28 15:43:40

137

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 28 Aug 2016 - 15:43

score 635 · Answer 8 · 2016-09-22 23:47:04

635

Views

About Fitting decomposition theorem of module

Published on 22 Sep 2016 - 23:47

score 531 · Answer 9 · 2016-09-29 23:23:08

531

Views

Techniques for Proving a Ring is Artinian?

Published on 29 Sep 2016 - 23:23

score 220 · Answer 10 · 2016-10-02 09:53:42

220

Views

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

Published on 02 Oct 2016 - 9:53

score 2k · Answer 11 · 2016-10-09 18:44:44

2k

Views

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

Published on 09 Oct 2016 - 18:44

score 219 · Answer 12 · 2016-10-09 22:03:56

219

Views

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

Published on 09 Oct 2016 - 22:03

score 437 · Answer 13 · 2016-10-25 13:03:48

437

Views

Structure theorem for commutative Noetherian rings

Published on 25 Oct 2016 - 13:03

score 2k · Answer 14 · 2016-11-10 15:35:56

2k

Views

Characterising subgroups of Prüfer $p$-groups.

Published on 10 Nov 2016 - 15:35

score 689 · Answer 15 · 2016-11-25 15:44:31

689

Views

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

Published on 25 Nov 2016 - 15:44

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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