List questions from free-modules

Published on 23 Dec 2021 - 15:03

326

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Question on $(2, 1+\sqrt{-5})$ as a submodule of $\mathbb{Z}[\sqrt{-5}]$.

Published on 28 Dec 2021 - 9:35

357

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Question related to "example of free module with bases of different cardinality"

Published on 24 Jan 2022 - 16:43

125

Views

If $N \leq M$, there exist free modules $F_N \leq N$, $F_M \leq M$ with $N = F_N \oplus N_{tor}$, $M = F_M \oplus M_{tor}$ with $F_N \leq F_M$

Published on 29 Jan 2022 - 6:12

116

Views

Software to determine if one ring is free over another

Published on 29 Mar 2026 - 9:10

193

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Quotient of a module is free implies the module is free

Published on 10 Feb 2022 - 8:39

74

Views

Reference request modules over a small category

Published on 28 Mar 2026 - 5:39

334

Views

Show if $M$ is free of rank $n$ as $R$-module, then $M/IM$ is free of rank $n$ as $R/I$ module

Published on 11 Feb 2022 - 16:26

99

Views

Localization of Cohen-Macaulay module of finite projective dimension at non-maximal prime ideal

Published on 25 Mar 2026 - 10:57

156

Views

Equivalent statements of a finitely generated module being locally free

Published on 23 Feb 2022 - 4:45

114

Views

Ideal generated by the entries of a representative matrix of a map between free modules

Published on 24 Feb 2022 - 2:13

57

Views

Phantom morphisms and Tor functor?

Published on 27 Mar 2026 - 23:30

82

Views

Is the ring $R$ a free module over $S$?

Published on 26 Feb 2022 - 2:38

74

Views

Can a matrix ring have a non-free ring extension?

Published on 26 Feb 2022 - 6:54

119

Views

About exactness of $Hom$ functor?

Published on 27 Mar 2026 - 23:32

List Question

Prove $D$ is $R$-algebra

Question on $(2, 1+\sqrt{-5})$ as a submodule of $\mathbb{Z}[\sqrt{-5}]$.

Question related to "example of free module with bases of different cardinality"

If $N \leq M$, there exist free modules $F_N \leq N$, $F_M \leq M$ with $N = F_N \oplus N_{tor}$, $M = F_M \oplus M_{tor}$ with $F_N \leq F_M$

Software to determine if one ring is free over another

Quotient of a module is free implies the module is free

Reference request modules over a small category

Show if $M$ is free of rank $n$ as $R$-module, then $M/IM$ is free of rank $n$ as $R/I$ module

Localization of Cohen-Macaulay module of finite projective dimension at non-maximal prime ideal

Equivalent statements of a finitely generated module being locally free

Ideal generated by the entries of a representative matrix of a map between free modules

Phantom morphisms and Tor functor?

Is the ring $R$ a free module over $S$?

Can a matrix ring have a non-free ring extension?

About exactness of $Hom$ functor?

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