Question

How Should I Prove this Function is Well-defined?

score 29 · Answer 1 · 2026-03-26 20:37:56

29

Views

How Should I Prove this Function is Well-defined?

Published on 26 Mar 2026 - 20:37

score 68 · Answer 2 · 2026-03-26 20:38:07

68

Views

If a Short Exact Sequence is Split-Exact, Does that Mean it is Left-Split?

Published on 26 Mar 2026 - 20:38

score 20 · Answer 3 · 2026-03-25 14:05:28

20

Views

counter-example for quotient of artinian and noetherian modules

Published on 25 Mar 2026 - 14:05

score 52 · Answer 4 · 2026-04-09 16:38:38

52

Views

How to find all $F[X]$-submodules of $\mathbb{R}^{2}$?

Published on 09 Apr 2026 - 16:38

score 63 · Answer 5 · 2026-04-16 13:26:14

63

Views

Proving that $M$ is finitely generated from exact sequence $ 0 \to M' \xrightarrow{f} M \xrightarrow{g} M'' \to 0 $

Published on 16 Apr 2026 - 13:26

score 315 · Answer 6 · 2026-04-14 01:44:36

315

Views

When is the restriction of scalars functor essentially surjective?

Published on 14 Apr 2026 - 1:44

score 59 · Answer 7 · 2026-03-25 14:06:24

59

Views

possibility of $\mathbb{Q}[x]$ being artinian as a quotient

Published on 25 Mar 2026 - 14:06

score 226 · Answer 8 · 2026-04-17 05:06:50

226

Views

Is ${\rm Hom}\left(\prod_{i\in{\cal I}}M_{i},N\right)\cong\bigoplus_{i\in{\cal I}}{\rm Hom}\left(M_{i},N\right)$ for modules?

Published on 17 Apr 2026 - 5:06

score 59 · Answer 9 · 2026-04-13 16:03:24

59

Views

Literature on Representation Theory of Graded Lie Algebras

Published on 13 Apr 2026 - 16:03

score 64 · Answer 10 · 2026-04-14 10:54:37

64

Views

Is Every Isomorphism on Tensor Product of Modules an R-module Isomorphism?

Published on 14 Apr 2026 - 10:54

score 99 · Answer 11 · 2026-04-11 05:34:35

99

Views

Step in proof of Structure theorem over PID - Jacobson, Basic Algebra I

Published on 11 Apr 2026 - 5:34

score 66 · Answer 12 · 2026-04-16 01:02:29

66

Views

Dimension argument for exact sequence of $\Bbb Z$-modules

Published on 16 Apr 2026 - 1:02

score 42 · Answer 13 · 2026-03-26 14:29:04

42

Views

How Can We Prove Flatness from an Induced Exact Sequence?

Published on 26 Mar 2026 - 14:29

score 29 · Answer 14 · 2026-04-15 18:20:31

29

Views

Has the Pontryagin dual of a module the same length of the original module?

Published on 15 Apr 2026 - 18:20

score 98 · Answer 15 · 2026-04-16 08:38:02

98

Views

Trouble with the hint: $g\circ \alpha \circ f'=0$ for an exercise on the $3\times3$ lemma

Published on 16 Apr 2026 - 8:38

List Question

How Should I Prove this Function is Well-defined?

If a Short Exact Sequence is Split-Exact, Does that Mean it is Left-Split?

counter-example for quotient of artinian and noetherian modules

How to find all $F[X]$-submodules of $\mathbb{R}^{2}$?

Proving that $M$ is finitely generated from exact sequence $ 0 \to M' \xrightarrow{f} M \xrightarrow{g} M'' \to 0 $

When is the restriction of scalars functor essentially surjective?

possibility of $\mathbb{Q}[x]$ being artinian as a quotient

Is ${\rm Hom}\left(\prod_{i\in{\cal I}}M_{i},N\right)\cong\bigoplus_{i\in{\cal I}}{\rm Hom}\left(M_{i},N\right)$ for modules?

Literature on Representation Theory of Graded Lie Algebras

Is Every Isomorphism on Tensor Product of Modules an R-module Isomorphism?

Step in proof of Structure theorem over PID - Jacobson, Basic Algebra I

Dimension argument for exact sequence of $\Bbb Z$-modules

How Can We Prove Flatness from an Induced Exact Sequence?

Has the Pontryagin dual of a module the same length of the original module?

Trouble with the hint: $g\circ \alpha \circ f'=0$ for an exercise on the $3\times3$ lemma

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