List questions from projective-module

Published on 10 Apr 2026 - 4:35

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vector bundles on the affine line over a PID

Published on 14 Apr 2026 - 20:37

1.3k

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Showing an ideal is a projective module via a split exact sequence

Published on 13 Apr 2026 - 22:04

141

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Projectivity of $\mathbb Q$ over $\mathbb Q\otimes_{\mathbb Z}\mathbb Q$

Published on 15 Apr 2026 - 19:45

8.5k

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Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?

Published on 16 Apr 2026 - 1:43

2.8k

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What is a projective ideal?

Published on 09 Apr 2026 - 0:38

973

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Resolutions of bimodules as $R^e$-modules.

Published on 12 Apr 2026 - 18:09

129

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If $f:M\to M,m\mapsto mr$ is injective, then show that $\text{Hom}_R(M,E)\stackrel{r}{\longrightarrow}\text{Hom}_R(M,E)$ is surjective

Published on 17 Apr 2026 - 5:04

86

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Map between finite projective modules are locally free

Published on 16 Apr 2026 - 1:47

17

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$UP = _fP$ is a projective $\mathbb{Z}S$-module.

Published on 15 Apr 2026 - 3:34

683

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Problem with split exact sequences and free finitely generated modules

Published on 13 Apr 2026 - 10:27

83

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Is every lattice in a number field projective over its ring of multipliers?

Published on 11 Apr 2026 - 16:12

51

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$Z\pi \cong Z\oplus Z$ and so $P \cong Z$

Published on 13 Apr 2026 - 20:38

53

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Does the decreasing sequence $Ma\supseteq Ma^2\supseteq\ldots\supseteq Ma^n\supseteq\ldots$ always stabilise when $R$ is artinian?

Published on 16 Apr 2026 - 5:07

51

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Prove that if $\zeta$ a torsion theory cogenerated by $U$, then $\zeta=(\ker \text{Hom}_R(-,U),\text{Cog}(U))$

Published on 16 Apr 2026 - 4:42

List Question

What is the relationship between various groups

vector bundles on the affine line over a PID

Showing an ideal is a projective module via a split exact sequence

Projectivity of $\mathbb Q$ over $\mathbb Q\otimes_{\mathbb Z}\mathbb Q$

Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?

What is a projective ideal?

Resolutions of bimodules as $R^e$-modules.

If $f:M\to M,m\mapsto mr$ is injective, then show that $\text{Hom}_R(M,E)\stackrel{r}{\longrightarrow}\text{Hom}_R(M,E)$ is surjective

Map between finite projective modules are locally free

$UP = _fP$ is a projective $\mathbb{Z}S$-module.

Problem with split exact sequences and free finitely generated modules

Is every lattice in a number field projective over its ring of multipliers?

$Z\pi \cong Z\oplus Z$ and so $P \cong Z$

Does the decreasing sequence $Ma\supseteq Ma^2\supseteq\ldots\supseteq Ma^n\supseteq\ldots$ always stabilise when $R$ is artinian?

Prove that if $\zeta$ a torsion theory cogenerated by $U$, then $\zeta=(\ker \text{Hom}_R(-,U),\text{Cog}(U))$

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