Question

Direct Sum of Projective and Free Modules

score 451 · Answer 1 · 2026-04-14 12:47:31

451

Views

Direct Sum of Projective and Free Modules

Published on 14 Apr 2026 - 12:47

score 60 · Answer 2 · 2026-05-11 04:36:17

60

Views

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

Published on 11 May 2026 - 4:36

score 294 · Answer 3 · 2026-04-15 19:22:57

294

Views

Local artinian ring and module with finite projective dimension

Published on 15 Apr 2026 - 19:22

score 2.9k · Answer 4 · 2026-04-09 13:00:00

2.9k

Views

Is $\mathbb{Z}_2$ a projective $\mathbb{Z}$-Module?

Published on 09 Apr 2026 - 13:00

score 352 · Answer 5 · 2026-04-15 01:09:40

352

Views

Example of module/ring with long projective resolution

Published on 15 Apr 2026 - 1:09

score 7.8k · Answer 6 · 2026-04-08 16:05:29

7.8k

Views

Calculating Ext and Tor for $\mathbb Z/m\mathbb Z$ and $\mathbb Z/n\mathbb Z$

Published on 08 Apr 2026 - 16:05

score 1.7k · Answer 7 · 2026-04-13 16:48:54

1.7k

Views

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

Published on 13 Apr 2026 - 16:48

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 937 · Answer 9 · 2026-04-12 04:32:19

937

Views

Projective and flat modules over polynomial rings

Published on 12 Apr 2026 - 4:32

score 116 · Answer 10 · 2026-04-14 08:51:06

116

Views

Projective R-modules.

Published on 14 Apr 2026 - 8:51

score 214 · Answer 11 · 2026-04-10 14:59:37

214

Views

The functor $\mathrm{Hom}(A,-)$ cannot commute with arbitrary direct sums for infinitely generated projective module $A$

Published on 10 Apr 2026 - 14:59

score 40 · Answer 12 · 2026-04-11 08:26:10

40

Views

In the definition of a projective object, when do we NOT lose generality from restricting the potential non-epi to an epi?

Published on 11 Apr 2026 - 8:26

score 136 · Answer 13 · 2026-04-10 10:30:08

136

Views

Understanding key step of dimension shifting proof in homological algebra

Published on 10 Apr 2026 - 10:30

score 201 · Answer 14 · 2026-04-09 12:20:49

201

Views

Prove that $\mathbb{Z}/ 3\mathbb{Z}$ is a projective $\mathbb{Z} / 6\mathbb{Z}$ module which is not free.

Published on 09 Apr 2026 - 12:20

score 119 · Answer 15 · 2026-04-11 16:12:17

119

Views

Is $C$ projective as $C[x]$ module?

Published on 11 Apr 2026 - 16:12

List Question

Direct Sum of Projective and Free Modules

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

Local artinian ring and module with finite projective dimension

Is $\mathbb{Z}_2$ a projective $\mathbb{Z}$-Module?

Example of module/ring with long projective resolution

Calculating Ext and Tor for $\mathbb Z/m\mathbb Z$ and $\mathbb Z/n\mathbb Z$

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

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

Projective and flat modules over polynomial rings

Projective R-modules.

The functor $\mathrm{Hom}(A,-)$ cannot commute with arbitrary direct sums for infinitely generated projective module $A$

In the definition of a projective object, when do we NOT lose generality from restricting the potential non-epi to an epi?

Understanding key step of dimension shifting proof in homological algebra

Prove that $\mathbb{Z}/ 3\mathbb{Z}$ is a projective $\mathbb{Z} / 6\mathbb{Z}$ module which is not free.

Is $C$ projective as $C[x]$ module?

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