List questions from free-modules

Published on 18 Mar 2020 - 13:35

147

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On a proof of generic freeness theorem

Published on 23 Mar 2020 - 17:44

35

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Condition for every faithful module to be free

Published on 24 Mar 2020 - 17:36

51

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Prove that if $X/A$ is a free module and if $A$ is a submodule of $X$, then $A$ is a direct summand of $X$

Published on 26 Mar 2020 - 18:17

49

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Does the isomorphism $\text{Ann}^M(1-ab)\cong \left(\text{Ann}^M(1-ab)\right)a$ always hold?

Published on 31 Mar 2020 - 18:38

208

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Prove that if a ring R has IBN, then so does R/ I for every proper two-sided ideal I.

Published on 01 Apr 2020 - 9:07

106

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If $m\otimes n=0$ when does it follow that $m=0$ or $n=0$?

Published on 02 Apr 2020 - 17:02

109

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Linearly independent elements among spanning elements in a free module

Published on 05 Apr 2020 - 10:13

130

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Existence of Tensor Product of Modules

Published on 08 Apr 2020 - 12:42

214

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If $\pi:M \to A^n$ is a surjection from $A$-module $M$ to free module $A^n$, then $M\cong A^n \oplus \ker\pi$.

Published on 08 Apr 2020 - 22:55

97

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If $R$ is IBN, do we have $K\oplus R^{n}\cong R^n\implies K=0$?

Published on 13 Apr 2020 - 11:07

198

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Proving that the tangent bundle of the sphere is projective but not free

Published on 20 Apr 2020 - 19:31

116

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symmetric power

Published on 25 Mar 2026 - 9:32

133

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Are finite projective modules locally free without axiom of choice?

Published on 26 Apr 2020 - 8:42

72

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Generalisation of $\text{ker}f \bigoplus \text{Im}f \cong M$

Published on 27 Apr 2020 - 16:46

List Question

Decomposing a module into a direct sum of torsion and free part?

On a proof of generic freeness theorem

Condition for every faithful module to be free

Prove that if $X/A$ is a free module and if $A$ is a submodule of $X$, then $A$ is a direct summand of $X$

Does the isomorphism $\text{Ann}^M(1-ab)\cong \left(\text{Ann}^M(1-ab)\right)a$ always hold?

Prove that if a ring R has IBN, then so does R/ I for every proper two-sided ideal I.

If $m\otimes n=0$ when does it follow that $m=0$ or $n=0$?

Linearly independent elements among spanning elements in a free module

Existence of Tensor Product of Modules

If $\pi:M \to A^n$ is a surjection from $A$-module $M$ to free module $A^n$, then $M\cong A^n \oplus \ker\pi$.

If $R$ is IBN, do we have $K\oplus R^{n}\cong R^n\implies K=0$?

Proving that the tangent bundle of the sphere is projective but not free

symmetric power

Are finite projective modules locally free without axiom of choice?

Generalisation of $\text{ker}f \bigoplus \text{Im}f \cong M$

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