Question

Direct Sum of Projective and Free Modules

score 448 · Answer 1 · 2017-02-26 19:52:02

448

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Direct Sum of Projective and Free Modules

Published on 26 Feb 2017 - 19:52

score 57 · Answer 2 · 2026-03-25 09:26:31

57

Views

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

Published on 25 Mar 2026 - 9:26

score 292 · Answer 3 · 2017-03-19 02:14:29

292

Views

Local artinian ring and module with finite projective dimension

Published on 19 Mar 2017 - 2:14

score 2.9k · Answer 4 · 2017-03-23 04:40:19

2.9k

Views

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

Published on 23 Mar 2017 - 4:40

score 350 · Answer 5 · 2026-03-26 09:39:00

350

Views

Example of module/ring with long projective resolution

Published on 26 Mar 2026 - 9:39

score 7.8k · Answer 6 · 2017-03-26 23:21:10

7.8k

Views

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

Published on 26 Mar 2017 - 23:21

score 1.7k · Answer 7 · 2017-03-31 16:30:31

1.7k

Views

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

Published on 31 Mar 2017 - 16:30

score 41 · Answer 8 · 2026-03-28 03:55:27

41

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 28 Mar 2026 - 3:55

score 935 · Answer 9 · 2026-03-26 12:52:11

935

Views

Projective and flat modules over polynomial rings

Published on 26 Mar 2026 - 12:52

score 114 · Answer 10 · 2017-04-08 22:25:48

114

Views

Projective R-modules.

Published on 08 Apr 2017 - 22:25

score 211 · Answer 11 · 2023-02-01 05:33:23

211

Views

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

Published on 01 Feb 2023 - 5:33

score 37 · Answer 12 · 2023-02-11 20:22:55

37

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 Feb 2023 - 20:22

score 134 · Answer 13 · 2026-03-26 06:30:56

134

Views

Understanding key step of dimension shifting proof in homological algebra

Published on 26 Mar 2026 - 6:30

score 199 · Answer 14 · 2023-03-16 11:26:09

199

Views

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

Published on 16 Mar 2023 - 11:26

score 116 · Answer 15 · 2023-03-31 19:41:35

116

Views

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

Published on 31 Mar 2023 - 19:41

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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