List questions from free-modules

46

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Let $\mathbb{C}[X]$ be a module over itself. Given $z \in \mathbb{C}$ define $M_z = \{ f \in \mathbb{C}[X] \ | \ f(z) = 0\}$. Give a basis for $M_z$

Published on 15 Apr 2026 - 19:16

299

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Linear dependence as an equivalence relation

Published on 13 Apr 2026 - 23:38

177

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Every projective module is a submodule of a free module?

Published on 14 Apr 2026 - 9:17

37

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How to prove that for $K$ $\mathbb{Z}$-free & $Q$ projective, $K\otimes_{\mathbb{Z}}Q$ is a projective?

Published on 11 Apr 2026 - 16:52

44

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If $V$ is free, show that $f$ is surjective.

Published on 14 Apr 2026 - 17:04

948

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Why is the $C^\infty(M)$-module of smooth sections of a vector bundle $E$ not free?

Published on 15 Apr 2026 - 1:15

726

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About dual of finitely generated projective module

Published on 10 Apr 2026 - 15:09

354

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The reason why FTFGMPID fails with UFD instead of PID

Published on 10 Apr 2026 - 8:08

109

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Axes of a free module over a PID

Published on 10 Apr 2026 - 21:48

245

Views

$\mathbb{Z}$-Module exercise

Published on 10 May 2026 - 14:27

61

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Axes of a free module over a PID (2)

Published on 14 Apr 2026 - 12:07

93

Views

Is $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ free?

Published on 13 Apr 2026 - 2:27

90

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If $R$ is an n-fir, why free $R$-modules of rank at most $n$ have unique rank?

Published on 16 Apr 2026 - 4:30

259

Views

Weird Definition about Presentations of Modules

Published on 07 Apr 2026 - 22:54

96

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When $M\simeq Ker \oplus Im$? Where $M$ is a Module

Published on 13 Apr 2026 - 16:17

List Question

Let $\mathbb{C}[X]$ be a module over itself. Given $z \in \mathbb{C}$ define $M_z = \{ f \in \mathbb{C}[X] \ | \ f(z) = 0\}$. Give a basis for $M_z$

Linear dependence as an equivalence relation

Every projective module is a submodule of a free module?

How to prove that for $K$ $\mathbb{Z}$-free & $Q$ projective, $K\otimes_{\mathbb{Z}}Q$ is a projective?

If $V$ is free, show that $f$ is surjective.

Why is the $C^\infty(M)$-module of smooth sections of a vector bundle $E$ not free?

About dual of finitely generated projective module

The reason why FTFGMPID fails with UFD instead of PID

Axes of a free module over a PID

$\mathbb{Z}$-Module exercise

Axes of a free module over a PID (2)

Is $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ free?

If $R$ is an n-fir, why free $R$-modules of rank at most $n$ have unique rank?

Weird Definition about Presentations of Modules

When $M\simeq Ker \oplus Im$? Where $M$ is a Module

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