Question

Proof that any element of a free abelian group which is not divisible by any $k>1$ can be extended to a basis

score 169 · Answer 1 · 2026-03-27 05:03:28

169

Views

Proof that any element of a free abelian group which is not divisible by any $k>1$ can be extended to a basis

Published on 27 Mar 2026 - 5:03

score 387 · Answer 2 · 2022-03-14 05:30:20

387

Views

Invariant basis number for matrix algebras

Published on 14 Mar 2022 - 5:30

score 39 · Answer 3 · 2022-03-17 14:42:16

39

Views

Basis for Module Over PID

Published on 17 Mar 2022 - 14:42

score 142 · Answer 4 · 2026-03-28 06:59:11

142

Views

Finitely generated projective $\mathbb{Z}[[x]]$-modules are free?

Published on 28 Mar 2026 - 6:59

score 49 · Answer 5 · 2026-03-28 00:48:05

49

Views

Some conclusions with respect to character module $M^{\ast}=Hom_{\mathbb{Z}}(M, \mathbb{Q/Z})$

Published on 28 Mar 2026 - 0:48

score 68 · Answer 6 · 2022-03-31 08:38:47

68

Views

Showing that a certain Tor group vanishes

Published on 31 Mar 2022 - 8:38

score 62 · Answer 7 · 2026-03-28 00:54:17

62

Views

Direct limit of n-presented modules?

Published on 28 Mar 2026 - 0:54

score 137 · Answer 8 · 2022-05-02 20:34:30

137

Views

I proved that submodules of free modules are sums of ideals. What's wrong?

Published on 02 May 2022 - 20:34

score 38 · Answer 9 · 2022-05-03 21:24:23

38

Views

Under what conditions would $S^{-1}F$ be a free left $S^{-1}R$-module?

Published on 03 May 2022 - 21:24

score 99 · Answer 10 · 2022-05-03 23:16:14

99

Views

$M/xM$ free over $R/xR$ implies $M$ is free over $R$ when $R$ Noetherian

Published on 03 May 2022 - 23:16

score 71 · Answer 11 · 2022-05-08 20:08:39

71

Views

Finding a basis for a free module

Published on 08 May 2022 - 20:08

score 56 · Answer 12 · 2026-03-28 07:15:48

56

Views

Equality of two free modules of the same finite rank under strong hypothesis.

Published on 28 Mar 2026 - 7:15

score 120 · Answer 13 · 2022-05-17 12:17:55

120

Views

Free objects in the category of all R-modules without linearly independent generating set

Published on 17 May 2022 - 12:17

score 39 · Answer 14 · 2026-03-27 23:37:57

39

Views

Finitness conditions under change of rings?

Published on 27 Mar 2026 - 23:37

score 112 · Answer 15 · 2022-05-28 16:25:51

112

Views

Show that $R/I\otimes_R I\cong R/I\oplus R/I$ and $\text{Frac } R\otimes_R I\cong \text{Frac } R$

Published on 28 May 2022 - 16:25

List Question

Proof that any element of a free abelian group which is not divisible by any $k>1$ can be extended to a basis

Invariant basis number for matrix algebras

Basis for Module Over PID

Finitely generated projective $\mathbb{Z}[[x]]$-modules are free?

Some conclusions with respect to character module $M^{\ast}=Hom_{\mathbb{Z}}(M, \mathbb{Q/Z})$

Showing that a certain Tor group vanishes

Direct limit of n-presented modules?

I proved that submodules of free modules are sums of ideals. What's wrong?

Under what conditions would $S^{-1}F$ be a free left $S^{-1}R$-module?

$M/xM$ free over $R/xR$ implies $M$ is free over $R$ when $R$ Noetherian

Finding a basis for a free module

Equality of two free modules of the same finite rank under strong hypothesis.

Free objects in the category of all R-modules without linearly independent generating set

Finitness conditions under change of rings?

Show that $R/I\otimes_R I\cong R/I\oplus R/I$ and $\text{Frac } R\otimes_R I\cong \text{Frac } R$

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