List questions from free-modules

Published on 02 May 2016 - 14:03

154

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A free module over $\Bbb C[x]$

Published on 18 Mar 2026 - 23:05

67

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Existence of alternative basis element in free module over a PID

Published on 07 Mar 2026 - 10:53

137

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Bases of free module of rank $2$

Published on 09 May 2016 - 11:23

9.9k

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$R=\{ m+nr\sqrt{2} \mid m,n \in \Bbb Z \}$ and $I_{a,b}=\{ ma+n(b+r\sqrt{2}) \mid m,n \in \Bbb Z \}$

Published on 23 Mar 2026 - 21:05

81

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Is $\mathbb{Z}[G^n]$ isomorphic to $\bigoplus_n\mathbb{Z}[G]$?

Published on 23 May 2016 - 1:28

178

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Is $\Bbb Z_2$ free?

Published on 25 Mar 2026 - 1:28

621

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Prove that an $R$-module $M$ is finitely generated if and only if...

Published on 06 Jun 2016 - 21:52

86

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About rank of free module compared to spanning and LI set

Published on 28 Mar 2026 - 3:34

1.5k

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Dimension of the rationals over the integers

Published on 15 Dec 2013 - 10:40

127

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Finding kernel of a map in a minimal free resolution of a graded ideal

Published on 26 Mar 2026 - 9:42

895

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All $\mathbb{Z}$-submodules of $\mathbb{Z}\oplus\mathbb{Z}$ are free.

Published on 21 Apr 2017 - 0:04

310

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A morphism of free modules that is an isomorphism upon dualization.

Published on 25 Apr 2017 - 20:01

157

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Why Jacobson radical of a cyclic module over integral domain $R$ such that $\mathrm{Rad}(R)=(0)$ is zero?

Published on 28 Mar 2026 - 12:14

474

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Direct product of projective modules

Published on 14 May 2017 - 7:25

List Question

Why abelian groups instead of modules in Algebraic Topology

A free module over $\Bbb C[x]$

Existence of alternative basis element in free module over a PID

Bases of free module of rank $2$

$R=\{ m+nr\sqrt{2} \mid m,n \in \Bbb Z \}$ and $I_{a,b}=\{ ma+n(b+r\sqrt{2}) \mid m,n \in \Bbb Z \}$

Is $\mathbb{Z}[G^n]$ isomorphic to $\bigoplus_n\mathbb{Z}[G]$?

Is $\Bbb Z_2$ free?

Prove that an $R$-module $M$ is finitely generated if and only if...

About rank of free module compared to spanning and LI set

Dimension of the rationals over the integers

Finding kernel of a map in a minimal free resolution of a graded ideal

All $\mathbb{Z}$-submodules of $\mathbb{Z}\oplus\mathbb{Z}$ are free.

A morphism of free modules that is an isomorphism upon dualization.

Why Jacobson radical of a cyclic module over integral domain $R$ such that $\mathrm{Rad}(R)=(0)$ is zero?

Direct product of projective modules

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