Question

Isomorphism $\epsilon \colon V \rightarrow V \oplus V$

score 94 · Answer 1 · 2026-04-15 21:18:42

94

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Isomorphism $\epsilon \colon V \rightarrow V \oplus V$

Published on 15 Apr 2026 - 21:18

score 28 · Answer 2 · 2026-04-16 16:18:28

28

Views

Every Cyclic Submodule of $M$ is Simple $\implies$ $M$ is Simple or the Ring of Homotheties on $M$ is a Division Ring

Published on 16 Apr 2026 - 16:18

score 78 · Answer 3 · 2026-04-15 14:52:03

78

Views

Showing that the rank of $M$ is exactly $1.$

Published on 15 Apr 2026 - 14:52

score 53 · Answer 4 · 2026-04-14 19:05:33

53

Views

Any artinian module is a finite direct sum of indecomposable modules

Published on 14 Apr 2026 - 19:05

score 33 · Answer 5 · 2026-04-14 03:21:26

33

Views

Deduce Jordan Normal Form from PID finitely generated module structure.

Published on 14 Apr 2026 - 3:21

score 65 · Answer 6 · 2026-04-13 17:32:32

65

Views

What exactly is the Jordan Canonical Form for the following matrix?

Published on 13 Apr 2026 - 17:32

score 105 · Answer 7 · 2026-04-14 06:24:48

105

Views

Terminology: submodule over subring

Published on 14 Apr 2026 - 6:24

score 44 · Answer 8 · 2026-04-16 02:03:50

44

Views

Exercise 10.28 from Altman & Kleiman's book

Published on 16 Apr 2026 - 2:03

score 62 · Answer 9 · 2026-04-15 00:23:27

62

Views

Show $E \cong E'$ as R-modules given $ h : N \to N'$ isomorphism, $\mathscr E : 0 \to N \to E \to M \to 0$ and its pushout

Published on 15 Apr 2026 - 0:23

score 69 · Answer 10 · 2026-04-17 04:12:11

69

Views

Is the category of graded modules over a graded-commutative ring an AB5 category?

Published on 17 Apr 2026 - 4:12

score 67 · Answer 11 · 2026-04-15 22:07:35

67

Views

$E$ :$k[t]$-mod. Show that either $E \cong M_\lambda \oplus M_\lambda$ or $E \cong M'_\lambda $.

Published on 15 Apr 2026 - 22:07

score 49 · Answer 12 · 2026-04-16 13:36:59

49

Views

Limit of diagram consisting of two maps $f: M \to N$ and $g: N \to M$ where $M,N$ are $R$-modules.

Published on 16 Apr 2026 - 13:36

score 87 · Answer 13 · 2026-04-14 08:44:11

87

Views

If a ring $A$ is a $D$-module. And If $A\cong B$ as rings. Then is $A\cong B$ as $D$-modules?

Published on 14 Apr 2026 - 8:44

score 59 · Answer 14 · 2026-04-12 12:59:40

59

Views

Matrices and Endomorphisms of finitely generated (but not free) Modules

Published on 12 Apr 2026 - 12:59

score 103 · Answer 15 · 2026-04-14 05:17:39

103

Views

Schur's Lemma of the Version for Lie Algebras

Published on 14 Apr 2026 - 5:17

List Question

Isomorphism $\epsilon \colon V \rightarrow V \oplus V$

Every Cyclic Submodule of $M$ is Simple $\implies$ $M$ is Simple or the Ring of Homotheties on $M$ is a Division Ring

Showing that the rank of $M$ is exactly $1.$

Any artinian module is a finite direct sum of indecomposable modules

Deduce Jordan Normal Form from PID finitely generated module structure.

What exactly is the Jordan Canonical Form for the following matrix?

Terminology: submodule over subring

Exercise 10.28 from Altman & Kleiman's book

Show $E \cong E'$ as R-modules given $ h : N \to N'$ isomorphism, $\mathscr E : 0 \to N \to E \to M \to 0$ and its pushout

Is the category of graded modules over a graded-commutative ring an AB5 category?

$E$ :$k[t]$-mod. Show that either $E \cong M_\lambda \oplus M_\lambda$ or $E \cong M'_\lambda $.

Limit of diagram consisting of two maps $f: M \to N$ and $g: N \to M$ where $M,N$ are $R$-modules.

If a ring $A$ is a $D$-module. And If $A\cong B$ as rings. Then is $A\cong B$ as $D$-modules?

Matrices and Endomorphisms of finitely generated (but not free) Modules

Schur's Lemma of the Version for Lie Algebras

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