Question

F.G. Projective Modules are Direct Summands of F.G. Free Modules?

score 590 · Answer 1 · 2026-04-16 23:26:36

590

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F.G. Projective Modules are Direct Summands of F.G. Free Modules?

Published on 16 Apr 2026 - 23:26

score 833 · Answer 2 · 2026-04-16 04:47:02

833

Views

Prove that (V,T) is a cyclic $F[x]$-module

Published on 16 Apr 2026 - 4:47

score 89 · Answer 3 · 2026-04-11 06:31:12

89

Views

Are filtrations given by comodules structures?

Published on 11 Apr 2026 - 6:31

score 489 · Answer 4 · 2026-04-16 09:40:17

489

Views

Showing $\mathbb{Q}\cong \mathbb{Q}\otimes_\mathbb{Z}\mathbb{Q}$.

Published on 16 Apr 2026 - 9:40

score 1.7k · Answer 5 · 2026-04-13 16:48:54

1.7k

Views

Projective modules and $\hom(P,\cdot)$

Published on 13 Apr 2026 - 16:48

score 347 · Answer 6 · 2026-04-11 03:39:54

347

Views

How to Find the automorphism group of the $A$-module $V$

Published on 11 Apr 2026 - 3:39

score 351 · Answer 7 · 2026-04-13 18:42:33

351

Views

Show that $\lvert \mathbb Z^n / N\rvert = \lvert \det (A) \rvert$.

Published on 13 Apr 2026 - 18:42

score 43 · Answer 8 · 2026-04-16 16:46:16

43

Views

If $0\rightarrow R^{\oplus a}\rightarrow M\rightarrow R^{\oplus b}\rightarrow 0$ is exact, then $M\simeq R^{\oplus (a+b)}$

Published on 16 Apr 2026 - 16:46

score 286 · Answer 9 · 2026-04-16 11:18:50

286

Views

$R$ and $R/radR$ have the same simple left modules.

Published on 16 Apr 2026 - 11:18

score 99 · Answer 10 · 2026-04-12 10:58:56

99

Views

Linear algebra question on similarity of linear transformations

Published on 12 Apr 2026 - 10:58

score 43 · Answer 11 · 2026-04-16 09:14:23

43

Views

For $M'\to M$, what are the induced maps $F\otimes M' \to F\otimes M$?

Published on 16 Apr 2026 - 9:14

score 292 · Answer 12 · 2026-04-14 04:28:53

292

Views

An example about finitely generated modules and finitely cogenerated modules

Published on 14 Apr 2026 - 4:28

score 45 · Answer 13 · 2026-04-14 01:39:10

45

Views

What is the meaning of saying following: Let $P$ be a finitely presented $A[X]$ module. Suppose $P$ is extended from $A$?

Published on 14 Apr 2026 - 1:39

score 481 · Answer 14 · 2026-04-08 18:11:33

481

Views

Flatness of subring

Published on 08 Apr 2026 - 18:11

score 41 · Answer 15 · 2026-04-08 22:46:29

41

Views

Difficulty with characterization of semisimplicity in terms of complements

Published on 08 Apr 2026 - 22:46

List Question

F.G. Projective Modules are Direct Summands of F.G. Free Modules?

Prove that (V,T) is a cyclic $F[x]$-module

Are filtrations given by comodules structures?

Showing $\mathbb{Q}\cong \mathbb{Q}\otimes_\mathbb{Z}\mathbb{Q}$.

Projective modules and $\hom(P,\cdot)$

How to Find the automorphism group of the $A$-module $V$

Show that $\lvert \mathbb Z^n / N\rvert = \lvert \det (A) \rvert$.

If $0\rightarrow R^{\oplus a}\rightarrow M\rightarrow R^{\oplus b}\rightarrow 0$ is exact, then $M\simeq R^{\oplus (a+b)}$

$R$ and $R/radR$ have the same simple left modules.

Linear algebra question on similarity of linear transformations

For $M'\to M$, what are the induced maps $F\otimes M' \to F\otimes M$?

An example about finitely generated modules and finitely cogenerated modules

What is the meaning of saying following: Let $P$ be a finitely presented $A[X]$ module. Suppose $P$ is extended from $A$?

Flatness of subring

Difficulty with characterization of semisimplicity in terms of complements

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