Question

Naturality in the Adjoint Property of Tensor Products

score 346 · Answer 1 · 2026-03-25 05:16:40

346

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Naturality in the Adjoint Property of Tensor Products

Published on 25 Mar 2026 - 5:16

score 701 · Answer 2 · 2018-02-21 02:36:05

701

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Prove that if a nonzero commutative ring R with identity has the property that every finitely generated R-module is free then R is a field.

Published on 21 Feb 2018 - 2:36

score 58 · Answer 3 · 2026-03-20 03:52:33

58

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Why can't a finitely generated module over a PID be generated by fewer elements than the number of invariant factors?

Published on 20 Mar 2026 - 3:52

score 818 · Answer 4 · 2018-02-21 20:32:31

818

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Suppose M is a module over integral domain R. If M is generated by k elements, then $rank(M) \leq k$ (Confirm my proof ?)

Published on 21 Feb 2018 - 20:32

score 106 · Answer 5 · 2018-02-22 22:34:05

106

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Prove Left Module Over Ring of Matrices is Cyclic

Published on 22 Feb 2018 - 22:34

score 76 · Answer 6 · 2026-03-25 12:53:21

76

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What does this paper means by $S$-homomorphism?

Published on 25 Mar 2026 - 12:53

score 64 · Answer 7 · 2026-03-24 15:31:34

64

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Splitting two exact sequences in a compatible way

Published on 24 Mar 2026 - 15:31

score 59 · Answer 8 · 2026-03-25 07:45:30

59

Views

Why is $Rad(P_S)/Soc(P_S)$ a direct sum of two uniserial modules?

Published on 25 Mar 2026 - 7:45

score 62 · Answer 9 · 2026-03-22 21:51:45

62

Views

A problem about split exact sequences.

Published on 22 Mar 2026 - 21:51

score 987 · Answer 10 · 2026-03-25 05:27:16

987

Views

When is every direct product of a ring also a free module?

Published on 25 Mar 2026 - 5:27

score 251 · Answer 11 · 2026-03-25 12:55:18

251

Views

Functor between modules over rings related by homomorphism

Published on 25 Mar 2026 - 12:55

score 45 · Answer 12 · 2026-03-20 06:00:52

45

Views

$\ell(M/N) \leq \ell(M)$ if $M$ is an $A$-module

Published on 20 Mar 2026 - 6:00

score 104 · Answer 13 · 2018-02-24 21:57:23

104

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Question about irreducible modules and the Artin-Wedderburn Theorem

Published on 24 Feb 2018 - 21:57

score 96 · Answer 14 · 2026-03-25 06:41:11

96

Views

Examples of torsion trace and torsion reject

Published on 25 Mar 2026 - 6:41

score 183 · Answer 15 · 2026-03-25 06:10:53

183

Views

Uniqueness of Jordan normal form via the Structure Theorem

Published on 25 Mar 2026 - 6:10

List Question

Naturality in the Adjoint Property of Tensor Products

Prove that if a nonzero commutative ring R with identity has the property that every finitely generated R-module is free then R is a field.

Why can't a finitely generated module over a PID be generated by fewer elements than the number of invariant factors?

Suppose M is a module over integral domain R. If M is generated by k elements, then $rank(M) \leq k$ (Confirm my proof ?)

Prove Left Module Over Ring of Matrices is Cyclic

What does this paper means by $S$-homomorphism?

Splitting two exact sequences in a compatible way

Why is $Rad(P_S)/Soc(P_S)$ a direct sum of two uniserial modules?

A problem about split exact sequences.

When is every direct product of a ring also a free module?

Functor between modules over rings related by homomorphism

$\ell(M/N) \leq \ell(M)$ if $M$ is an $A$-module

Question about irreducible modules and the Artin-Wedderburn Theorem

Examples of torsion trace and torsion reject

Uniqueness of Jordan normal form via the Structure Theorem

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