Question

If P is a R-module, what is the difference between the Free modules F(P) and P?

score 46 · Answer 1 · 2026-04-15 09:10:05

46

Views

If P is a R-module, what is the difference between the Free modules F(P) and P?

Published on 15 Apr 2026 - 9:10

score 2.2k · Answer 2 · 2026-04-16 15:55:41

2.2k

Views

If $P$ is a finitely generated projective $R$-Module, then $\operatorname{Hom}_R(P,R)$ is projective.

Published on 16 Apr 2026 - 15:55

score 244 · Answer 3 · 2026-04-15 20:34:08

244

Views

Isomorphic Submodules implies Isomorphic Quotients?

Published on 15 Apr 2026 - 20:34

score 413 · Answer 4 · 2026-04-14 18:07:25

413

Views

Is $D\otimes_{R}A\cong \mathrm{Hom}_{R}(D,A)$ ever true if $D$ is a projective $R$-module?

Published on 14 Apr 2026 - 18:07

score 138 · Answer 5 · 2026-04-14 01:28:59

138

Views

Is the intersection of the kernels of all the linear forms trivial?

Published on 14 Apr 2026 - 1:28

score 140 · Answer 6 · 2026-04-12 11:51:53

140

Views

Is an element in a module that is annihilated by all the scalars necessarily zero?

Published on 12 Apr 2026 - 11:51

score 496 · Answer 7 · 2026-04-16 13:31:44

496

Views

Rank of a free module

Published on 16 Apr 2026 - 13:31

score 151 · Answer 8 · 2026-04-15 04:06:34

151

Views

Multigraded free module over multigraded ring has multihomogeneous basis?

Published on 15 Apr 2026 - 4:06

score 95 · Answer 9 · 2026-04-14 03:34:03

95

Views

Does $\operatorname{End}_R(R)\cong R^{\text{op}}$ still hold when $R$ doesn't have an identity?

Published on 14 Apr 2026 - 3:34

score 81 · Answer 10 · 2026-04-15 22:49:03

81

Views

$L[G]\otimes_{K[G]} M \cong L[G]\otimes_{K[G]} N \Rightarrow M \cong N$

Published on 15 Apr 2026 - 22:49

score 100 · Answer 11 · 2026-04-13 22:04:02

100

Views

How to decompose this finitely generated module over $k[x]$?

Published on 13 Apr 2026 - 22:04

score 142 · Answer 12 · 2026-04-10 16:44:15

142

Views

Trouble Understanding Hom, Modules, and SES

Published on 10 Apr 2026 - 16:44

score 67 · Answer 13 · 2026-04-13 13:48:00

67

Views

How can I prove if $R$ is a domain where every submodule is a summand, then it is a field?

Published on 13 Apr 2026 - 13:48

score 267 · Answer 14 · 2026-04-15 09:05:57

267

Views

Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules

Published on 15 Apr 2026 - 9:05

score 2.2k · Answer 15 · 2026-04-08 02:47:09

2.2k

Views

How does a matrix define a module?

Published on 08 Apr 2026 - 2:47

List Question

If P is a R-module, what is the difference between the Free modules F(P) and P?

If $P$ is a finitely generated projective $R$-Module, then $\operatorname{Hom}_R(P,R)$ is projective.

Isomorphic Submodules implies Isomorphic Quotients?

Is $D\otimes_{R}A\cong \mathrm{Hom}_{R}(D,A)$ ever true if $D$ is a projective $R$-module?

Is the intersection of the kernels of all the linear forms trivial?

Is an element in a module that is annihilated by all the scalars necessarily zero?

Rank of a free module

Multigraded free module over multigraded ring has multihomogeneous basis?

Does $\operatorname{End}_R(R)\cong R^{\text{op}}$ still hold when $R$ doesn't have an identity?

$L[G]\otimes_{K[G]} M \cong L[G]\otimes_{K[G]} N \Rightarrow M \cong N$

How to decompose this finitely generated module over $k[x]$?

Trouble Understanding Hom, Modules, and SES

How can I prove if $R$ is a domain where every submodule is a summand, then it is a field?

Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules

How does a matrix define a module?

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