Question

How can one express $\mathbb{Q} / \mathbb{Z}$ as a direct sum of $\mathbb{Q}$ and $\mathbb{Z} / p$ for $p$ prime?

score 232 · Answer 1 · 2019-05-23 10:26:08

232

Views

How can one express $\mathbb{Q} / \mathbb{Z}$ as a direct sum of $\mathbb{Q}$ and $\mathbb{Z} / p$ for $p$ prime?

Published on 23 May 2019 - 10:26

score 376 · Answer 2 · 2019-05-29 14:51:50

376

Views

The category of finitely generated abelian groups does not have enough injectives

Published on 29 May 2019 - 14:51

score 95 · Answer 3 · 2019-06-03 15:31:45

95

Views

Prove that $\varphi$ is an isomorphism.

Published on 03 Jun 2019 - 15:31

score 152 · Answer 4 · 2019-06-03 18:29:13

152

Views

A module $N$ is semisimple $\Longleftrightarrow$ $N$ has no proper essential submodules

Published on 03 Jun 2019 - 18:29

score 231 · Answer 5 · 2019-06-09 09:40:14

231

Views

Prove $F[x]/(x^n)$ is an injective module

Published on 09 Jun 2019 - 9:40

score 190 · Answer 6 · 2026-03-25 09:24:39

190

Views

$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Published on 25 Mar 2026 - 9:24

score 55 · Answer 7 · 2019-08-09 11:51:25

55

Views

Is $\operatorname{Quot}(R)/R$ an injective $R$-Module?

Published on 09 Aug 2019 - 11:51

score 80 · Answer 8 · 2019-08-29 22:23:52

80

Views

$R$ is a noetherian ring and $I$ is an injective $R$-module. Let $J\subset R$ be an ideal. Then $I_1=\{x\in I\mid\exists n,J^nx=0\}$ is injective.

Published on 29 Aug 2019 - 22:23

score 741 · Answer 9 · 2019-09-22 03:32:22

741

Views

Over an integral domain is a module injective iff it is divisible?

Published on 22 Sep 2019 - 3:32

score 371 · Answer 10 · 2019-09-26 00:18:42

371

Views

Projective and injective objects

Published on 26 Sep 2019 - 0:18

score 208 · Answer 11 · 2014-03-12 04:36:18

208

Views

Projective and Injective Modules

Published on 12 Mar 2014 - 4:36

score 138 · Answer 12 · 2014-03-31 06:57:12

138

Views

Is the following abelian group injective?

Published on 31 Mar 2014 - 6:57

score 135 · Answer 13 · 2014-04-30 09:34:45

135

Views

If a left ideal of R is a direct summand of R, is I an injective R-module?

Published on 30 Apr 2014 - 9:34

score 111 · Answer 14 · 2014-04-30 09:41:10

111

Views

If a left ideal I of R is an injective R-module then I is a projective R-module. Is the converse true?

Published on 30 Apr 2014 - 9:41

score 514 · Answer 15 · 2014-05-05 20:41:30

514

Views

Is there an analogue of Bass-Papp theorem for Projective modules?

Published on 05 May 2014 - 20:41

List Question

How can one express $\mathbb{Q} / \mathbb{Z}$ as a direct sum of $\mathbb{Q}$ and $\mathbb{Z} / p$ for $p$ prime?

The category of finitely generated abelian groups does not have enough injectives

Prove that $\varphi$ is an isomorphism.

A module $N$ is semisimple $\Longleftrightarrow$ $N$ has no proper essential submodules

Prove $F[x]/(x^n)$ is an injective module

$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Is $\operatorname{Quot}(R)/R$ an injective $R$-Module?

$R$ is a noetherian ring and $I$ is an injective $R$-module. Let $J\subset R$ be an ideal. Then $I_1=\{x\in I\mid\exists n,J^nx=0\}$ is injective.

Over an integral domain is a module injective iff it is divisible?

Projective and injective objects

Projective and Injective Modules

Is the following abelian group injective?

If a left ideal of R is a direct summand of R, is I an injective R-module?

If a left ideal I of R is an injective R-module then I is a projective R-module. Is the converse true?

Is there an analogue of Bass-Papp theorem for Projective modules?

Trending Questions

Popular # Hahtags

Popular Questions