Question

Existence of module homomorphism $\phi : M \rightarrow N$ such that $\Phi =\phi^2$

score 146 · Answer 1 · 2014-08-11 22:07:30

146

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Existence of module homomorphism $\phi : M \rightarrow N$ such that $\Phi =\phi^2$

Published on 11 Aug 2014 - 22:07

score 265 · Answer 2 · 2026-03-25 07:44:54

265

Views

Consider $\mathbf{Z}G$, $G$ finite. If the characters of two $\mathbf{Z}G$-modules are equal, does it follow that the modules are isomorphic?

Published on 25 Mar 2026 - 7:44

score 73 · Answer 3 · 2026-03-26 14:34:41

73

Views

$0\to L\to M\to N\to 0 $ is split if $0\to {\rm Hom}_R(D,L)\to {\rm Hom}_R(D,M)\to {\rm Hom}_R(D,N)\to 0$ is exact for any $D$.

Published on 26 Mar 2026 - 14:34

score 189 · Answer 4 · 2014-08-13 18:47:03

189

Views

If $R$ is a domain and $M$ a finitely generated $R$-module, is it true that $\bigcap_{f\in M^{*}}\ker{f}=\operatorname{Tor}M$?

Published on 13 Aug 2014 - 18:47

score 46 · Answer 5 · 2026-03-26 11:01:33

46

Views

Why does $\rho_{\mathbf{Z}^t\otimes P}=\rho_R$ imply the isomorphsim of $\mathbf{Z}^t\otimes P\cong R$?

Published on 26 Mar 2026 - 11:01

score 125 · Answer 6 · 2026-03-28 01:25:56

125

Views

Help understanding statement relating to structure of modules over PIDs

Published on 28 Mar 2026 - 1:25

score 975 · Answer 7 · 2014-08-14 05:18:48

975

Views

Tensor product and its homomorphisms.

Published on 14 Aug 2014 - 5:18

score 2.4k · Answer 8 · 2014-08-14 14:07:20

2.4k

Views

Are $\mathbb{Q}$ or $\mathbb{Z}$ flat modules?

Published on 14 Aug 2014 - 14:07

score 103 · Answer 9 · 2014-08-14 15:50:34

103

Views

Characterization of projective modules.

Published on 14 Aug 2014 - 15:50

score 246 · Answer 10 · 2014-08-14 23:41:39

246

Views

Isomorphism of a torsion product and a quotioten of torsion product.

Published on 14 Aug 2014 - 23:41

score 91 · Answer 11 · 2014-08-15 05:35:39

91

Views

$A\otimes_RB$ is an $R$-algebra

Published on 15 Aug 2014 - 5:35

score 89 · Answer 12 · 2014-08-15 14:01:48

89

Views

Finding a suitable basis for a vector space

Published on 15 Aug 2014 - 14:01

score 430 · Answer 13 · 2014-08-15 16:53:23

430

Views

Infinite dimensional Vector Spaces and Bases of Quotients

Published on 15 Aug 2014 - 16:53

score 33 · Answer 14 · 2014-08-15 17:43:17

33

Views

Submodule Equality

Published on 15 Aug 2014 - 17:43

score 52 · Answer 15 · 2026-03-26 01:06:39

52

Views

Is this ring Noetherian

Published on 26 Mar 2026 - 1:06

List Question

Existence of module homomorphism $\phi : M \rightarrow N$ such that $\Phi =\phi^2$

Consider $\mathbf{Z}G$, $G$ finite. If the characters of two $\mathbf{Z}G$-modules are equal, does it follow that the modules are isomorphic?

$0\to L\to M\to N\to 0 $ is split if $0\to {\rm Hom}_R(D,L)\to {\rm Hom}_R(D,M)\to {\rm Hom}_R(D,N)\to 0$ is exact for any $D$.

If $R$ is a domain and $M$ a finitely generated $R$-module, is it true that $\bigcap_{f\in M^{*}}\ker{f}=\operatorname{Tor}M$?

Why does $\rho_{\mathbf{Z}^t\otimes P}=\rho_R$ imply the isomorphsim of $\mathbf{Z}^t\otimes P\cong R$?

Help understanding statement relating to structure of modules over PIDs

Tensor product and its homomorphisms.

Are $\mathbb{Q}$ or $\mathbb{Z}$ flat modules?

Characterization of projective modules.

Isomorphism of a torsion product and a quotioten of torsion product.

$A\otimes_RB$ is an $R$-algebra

Finding a suitable basis for a vector space

Infinite dimensional Vector Spaces and Bases of Quotients

Submodule Equality

Is this ring Noetherian

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