List questions from modules

Published on 21 May 2020 - 12:35

121

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If $aR$ is free, how can I conclude $a$ is not a zero divisor?

Published on 12 Apr 2026 - 0:37

157

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Localisation map is zero or injective, then zero ideal is primary.

Published on 25 Mar 2026 - 9:23

95

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Miles Reid Commutative Algebra exercise 3.3 (Noetherian rings)

Published on 05 Apr 2026 - 14:18

105

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When is $K[X_1,X_2,...,X_n] \to K[Y_1,Y_2,...,Y_m]$ a flat morphism

Published on 26 Mar 2026 - 2:47

34

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Question about a step in the proof of the uniqueness of the decomposition of a finitely generated R-module, R a PID.

Published on 27 Mar 2026 - 14:03

89

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Split exact short sequence

Published on 27 Mar 2026 - 14:57

176

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Split and non splitting short exact sequence

Published on 27 Mar 2026 - 13:17

101

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Split exact sequence of linear maps implies split exact sequence of linear hom maps

Published on 27 Mar 2026 - 13:18

305

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Induced module; what is the $K[G]$-action?

Published on 29 Mar 2026 - 16:39

240

Views

Universal property of direct product

Published on 23 May 2020 - 18:52

21

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Proof of a left R-module M is free with basis X iff M is internal direct summand of Rx where x is in X

Published on 23 May 2020 - 19:40

121

Views

The module $\text{Hom}_C(E,F)$ of two finitely generated projective $C$-modules

Published on 27 Mar 2026 - 14:10

61

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Proving the analogous of $a\subseteq r(a)$ for $r_M(N)$

Published on 05 Apr 2026 - 17:03

83

Views

A module over a non-commutative ring may have bases with different number of elements

Published on 24 May 2020 - 8:11

List Question

In a PID, every principal ideal is free

If $aR$ is free, how can I conclude $a$ is not a zero divisor?

Localisation map is zero or injective, then zero ideal is primary.

Miles Reid Commutative Algebra exercise 3.3 (Noetherian rings)

When is $K[X_1,X_2,...,X_n] \to K[Y_1,Y_2,...,Y_m]$ a flat morphism

Question about a step in the proof of the uniqueness of the decomposition of a finitely generated R-module, R a PID.

Split exact short sequence

Split and non splitting short exact sequence

Split exact sequence of linear maps implies split exact sequence of linear hom maps

Induced module; what is the $K[G]$-action?

Universal property of direct product

Proof of a left R-module M is free with basis X iff M is internal direct summand of Rx where x is in X

The module $\text{Hom}_C(E,F)$ of two finitely generated projective $C$-modules

Proving the analogous of $a\subseteq r(a)$ for $r_M(N)$

A module over a non-commutative ring may have bases with different number of elements

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