Question

Decomposing a group as a direct product of its kernel and image

score 411 · Answer 1 · 2026-03-26 14:25:01

411

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Decomposing a group as a direct product of its kernel and image

Published on 26 Mar 2026 - 14:25

score 88 · Answer 2 · 2026-03-26 04:36:25

88

Views

If $I$ injective then $\operatorname{Hom}_R(M,I)=0$ imply $M=0$?

Published on 26 Mar 2026 - 4:36

score 1.4k · Answer 3 · 2026-03-27 03:49:01

1.4k

Views

Contravariant Hom Functor is Left Exact

Published on 27 Mar 2026 - 3:49

score 60 · Answer 4 · 2026-04-11 00:46:06

60

Views

Bimodule over division algebras

Published on 11 Apr 2026 - 0:46

score 233 · Answer 5 · 2026-04-10 22:47:35

233

Views

Equivariant maps between real linear representations of finitely generated groups

Published on 10 Apr 2026 - 22:47

score 101 · Answer 6 · 2026-03-27 22:03:27

101

Views

Unique 2-dimensional irreducible representation

Published on 27 Mar 2026 - 22:03

score 154 · Answer 7 · 2026-03-27 08:56:41

154

Views

Colon ideal and Cyclic modules

Published on 27 Mar 2026 - 8:56

score 53 · Answer 8 · 2026-03-25 16:02:32

53

Views

Checking that $\dfrac{\mathbb{Z}[x_1,x_2]}{\langle x_1^2\rangle}$ is a $\mathbb{Z}$-algebra

Published on 25 Mar 2026 - 16:02

score 87 · Answer 9 · 2026-04-07 09:39:59

87

Views

Why isn't it true that every finitely generated module is also projective?

Published on 07 Apr 2026 - 9:39

score 504 · Answer 10 · 2026-03-27 23:30:06

504

Views

Projective modules and lifting property

Published on 27 Mar 2026 - 23:30

score 49 · Answer 11 · 2026-04-09 10:05:41

49

Views

Each magma $M$ is associated with monoids $\mathcal{L}(M)$ and $\mathcal{R}(M)$. What are these called, and have they been studied?

Published on 09 Apr 2026 - 10:05

score 152 · Answer 12 · 2026-03-25 12:48:55

152

Views

$A$-linear maps between $A$-modules where $A$ is a $K$-algebra and $K$ is a commutative ring

Published on 25 Mar 2026 - 12:48

score 174 · Answer 13 · 2020-03-30 04:26:16

174

Views

An exercise in Rings and Their Modules by Paul E. Bland

Published on 30 Mar 2020 - 4:26

score 16 · Answer 14 · 2020-03-30 09:38:00

16

Views

For any $R$-submodule $N$ of $M$, $N=Ma~\text{ if and only if}~ N=MaR,a\in R.$

Published on 30 Mar 2020 - 9:38

score 96 · Answer 15 · 2026-04-10 16:26:47

96

Views

Is there exists a module which is not completely decomposable

Published on 10 Apr 2026 - 16:26

List Question

Decomposing a group as a direct product of its kernel and image

If $I$ injective then $\operatorname{Hom}_R(M,I)=0$ imply $M=0$?

Contravariant Hom Functor is Left Exact

Bimodule over division algebras

Equivariant maps between real linear representations of finitely generated groups

Unique 2-dimensional irreducible representation

Colon ideal and Cyclic modules

Checking that $\dfrac{\mathbb{Z}[x_1,x_2]}{\langle x_1^2\rangle}$ is a $\mathbb{Z}$-algebra

Why isn't it true that every finitely generated module is also projective?

Projective modules and lifting property

Each magma $M$ is associated with monoids $\mathcal{L}(M)$ and $\mathcal{R}(M)$. What are these called, and have they been studied?

$A$-linear maps between $A$-modules where $A$ is a $K$-algebra and $K$ is a commutative ring

An exercise in Rings and Their Modules by Paul E. Bland

For any $R$-submodule $N$ of $M$, $N=Ma~\text{ if and only if}~ N=MaR,a\in R.$

Is there exists a module which is not completely decomposable

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