Question

Does sub-module of free module over PID is free require commutativity?

score 78 · Answer 1 · 2023-05-17 04:24:22

78

Views

Does sub-module of free module over PID is free require commutativity?

Published on 17 May 2023 - 4:24

score 37 · Answer 2 · 2023-05-26 02:15:55

37

Views

Finitely-Generated modules over a commutative ring with $1$.

Published on 26 May 2023 - 2:15

score 39 · Answer 3 · 2023-06-25 14:14:03

39

Views

$R[x]/(f)$ is free over $R$ implies that $R[x]/(f) \to Q \otimes R[x]/(f)$ is a monomorphism

Published on 25 Jun 2023 - 14:14

score 172 · Answer 4 · 2023-06-29 13:50:48

172

Views

Change of basis in general free modules

Published on 29 Jun 2023 - 13:50

score 126 · Answer 5 · 2023-06-29 19:19:16

126

Views

Exact conditions so that vector-space-like change of basis is possible in a free module

Published on 29 Jun 2023 - 19:19

score 54 · Answer 6 · 2023-06-29 22:13:05

54

Views

Proving that a subset of a free module is a basis using category theory.

Published on 29 Jun 2023 - 22:13

score 41 · Answer 7 · 2023-06-30 00:05:45

41

Views

Prove a set is a basis for a free module if its elements share coefficients with an actual basis.

Published on 30 Jun 2023 - 0:05

score 76 · Answer 8 · 2023-07-28 19:22:40

76

Views

How is $\text{Tor}_1^{\mathbb{Z}}(X,R)$ defined in a simple manner as an R-module?

Published on 28 Jul 2023 - 19:22

score 65 · Answer 9 · 2023-07-31 14:07:56

65

Views

Rank and dimension dilemma for modules

Published on 31 Jul 2023 - 14:07

score 43 · Answer 10 · 2026-03-26 20:36:36

43

Views

Understanding excision with another approach

Published on 26 Mar 2026 - 20:36

score 10 · Answer 11 · 2023-08-16 10:09:09

10

Views

Embedding of a topologically free algebra in another topologically free algebra

Published on 16 Aug 2023 - 10:09

score 135 · Answer 12 · 2023-08-17 09:36:03

135

Views

Eisenbud Exercises 1.22 & 1.23 - Understanding Free Resolutions

Published on 17 Aug 2023 - 9:36

score 42 · Answer 13 · 2023-08-20 11:35:11

42

Views

If $A$ and $C$ are free modules and $C$=$A \oplus B$, need $B$ be free?

Published on 20 Aug 2023 - 11:35

score 18 · Answer 14 · 2026-03-20 07:20:53

18

Views

Find size of equivalent class of word

Published on 20 Mar 2026 - 7:20

score 56 · Answer 15 · 2023-08-28 23:33:41

56

Views

rank of a free submodule of a free module of infinite rank

Published on 28 Aug 2023 - 23:33

List Question

Does sub-module of free module over PID is free require commutativity?

Finitely-Generated modules over a commutative ring with $1$.

$R[x]/(f)$ is free over $R$ implies that $R[x]/(f) \to Q \otimes R[x]/(f)$ is a monomorphism

Change of basis in general free modules

Exact conditions so that vector-space-like change of basis is possible in a free module

Proving that a subset of a free module is a basis using category theory.

Prove a set is a basis for a free module if its elements share coefficients with an actual basis.

How is $\text{Tor}_1^{\mathbb{Z}}(X,R)$ defined in a simple manner as an R-module?

Rank and dimension dilemma for modules

Understanding excision with another approach

Embedding of a topologically free algebra in another topologically free algebra

Eisenbud Exercises 1.22 & 1.23 - Understanding Free Resolutions

If $A$ and $C$ are free modules and $C$=$A \oplus B$, need $B$ be free?

Find size of equivalent class of word

rank of a free submodule of a free module of infinite rank

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