Question

If $P$ is a fg projective $\mathbb{Z}[G]$-module, what is $P\otimes\mathbb{R}$?

score 59 · Answer 1 · 2026-04-15 06:17:28

59

Views

If $P$ is a fg projective $\mathbb{Z}[G]$-module, what is $P\otimes\mathbb{R}$?

Published on 15 Apr 2026 - 6:17

score 134 · Answer 2 · 2026-04-13 21:37:16

134

Views

Prove the primary decomposition is irredundant

Published on 13 Apr 2026 - 21:37

score 751 · Answer 3 · 2026-04-14 05:17:28

751

Views

Expressing the action of the dihedral group D4's generators as matrices, with respect to a certain basis.

Published on 14 Apr 2026 - 5:17

score 90 · Answer 4 · 2026-04-14 15:55:49

90

Views

Showing that a two-dimensional unitary commutative algebra over $\mathbb{R}$ has a certain basis.

Published on 14 Apr 2026 - 15:55

score 224 · Answer 5 · 2026-04-16 06:09:26

224

Views

In the proof of split short exact sequence, when $\sigma \alpha = \text{id}_A$, then the sequence is split.

Published on 16 Apr 2026 - 6:09

score 644 · Answer 6 · 2026-04-13 22:11:49

644

Views

Tensor Products of Modules (restriction and extension of scalars)

Published on 13 Apr 2026 - 22:11

score 78 · Answer 7 · 2026-04-16 04:01:56

78

Views

Why is $R\mapsto\operatorname{End}_{R-lin}(R\otimes_k V)$ representable by $\operatorname{Sym}(V\otimes_k V^\vee)$?

Published on 16 Apr 2026 - 4:01

score 991 · Answer 8 · 2026-04-14 09:08:07

991

Views

Over a principal ideal domain $R$, a submodule $N$ of a finitely-generated $R-$module M is finitely-generated.

Published on 14 Apr 2026 - 9:08

score 209 · Answer 9 · 2026-04-16 00:48:17

209

Views

Proving map between Hom Set surjective implies map between modules injective

Published on 16 Apr 2026 - 0:48

score 419 · Answer 10 · 2026-04-08 21:29:55

419

Views

What is a Module, and what is an R-module? (understanding the definition)

Published on 08 Apr 2026 - 21:29

score 272 · Answer 11 · 2026-04-17 05:04:10

272

Views

If bimodules are important, why not bi-vector spaces?

Published on 17 Apr 2026 - 5:04

score 83 · Answer 12 · 2026-04-12 04:45:41

83

Views

Question about the definition of free modules

Published on 12 Apr 2026 - 4:45

score 128 · Answer 13 · 2026-04-14 23:41:57

128

Views

Let $N$ be an $R$-module, $I$ be a set and $\left \{ M_i:i \in I\right \}$ a collection of $R$-modules. Show that the injective functions...

Published on 14 Apr 2026 - 23:41

score 2.8k · Answer 14 · 2026-04-17 07:29:19

2.8k

Views

Let $R$ be a ring, and let $V$ denote the $R$-Module $R$. Determine all module homomorphisms (need clarification of some concepts)

Published on 17 Apr 2026 - 7:29

score 345 · Answer 15 · 2026-04-14 16:28:29

345

Views

Given $A \rightarrow B$ morphism we have $B \otimes_A M$ is flat given that $M$ is flat

Published on 14 Apr 2026 - 16:28

List Question

If $P$ is a fg projective $\mathbb{Z}[G]$-module, what is $P\otimes\mathbb{R}$?

Prove the primary decomposition is irredundant

Expressing the action of the dihedral group D4's generators as matrices, with respect to a certain basis.

Showing that a two-dimensional unitary commutative algebra over $\mathbb{R}$ has a certain basis.

In the proof of split short exact sequence, when $\sigma \alpha = \text{id}_A$, then the sequence is split.

Tensor Products of Modules (restriction and extension of scalars)

Why is $R\mapsto\operatorname{End}_{R-lin}(R\otimes_k V)$ representable by $\operatorname{Sym}(V\otimes_k V^\vee)$?

Over a principal ideal domain $R$, a submodule $N$ of a finitely-generated $R-$module M is finitely-generated.

Proving map between Hom Set surjective implies map between modules injective

What is a Module, and what is an R-module? (understanding the definition)

If bimodules are important, why not bi-vector spaces?

Question about the definition of free modules

Let $N$ be an $R$-module, $I$ be a set and $\left \{ M_i:i \in I\right \}$ a collection of $R$-modules. Show that the injective functions...

Let $R$ be a ring, and let $V$ denote the $R$-Module $R$. Determine all module homomorphisms (need clarification of some concepts)

Given $A \rightarrow B$ morphism we have $B \otimes_A M$ is flat given that $M$ is flat

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