List questions from free-modules

Published on 17 May 2021 - 15:15

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Proof Verification: $R[S]$ is a projective $R-$module (S is an arbitrary nonempty set)

Published on 25 May 2021 - 1:34

76

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Extracting Rank from a module isomorphism over a PID

Published on 16 Jun 2021 - 0:26

166

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Prove $(X,Y) \subset \mathbb{C}[X,Y]$ is not free as $\mathbb{C}[X,Y]$-module using two isomorphisms

Published on 17 Jun 2021 - 9:09

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Every projective module is a direct summand of free module.

Published on 22 Jun 2021 - 10:22

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Smallest direct summand containing a submodule

Published on 05 Jul 2021 - 8:45

56

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Lazard theorem, one direction

Published on 27 Mar 2026 - 20:12

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Prove $M$ is not free

Published on 11 Aug 2021 - 20:01

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Subgroups of $\mathbb{Z} \times \mathbb{Z}$ of index $p$ and $pq$

Published on 14 Aug 2021 - 14:08

108

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Isomorphism of vector spaces over the quotient of a ring

Published on 15 Aug 2021 - 13:48

79

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Universal splitting algebra of a monic polynomial over a field is a field?

Published on 15 Aug 2021 - 14:50

87

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About condition of homomorphism between $\mathbb{Z}[G]$-modules (free as $\mathbb{Z}$-module) factors through free $\mathbb{Z}[G]$-module

Published on 12 Sep 2021 - 11:34

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Consider $R=M_{n}(k)$ which $k$ is a field. Properties of $M$ as an $R$-Module.

Published on 22 Sep 2021 - 17:21

155

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If a module is second syzygy and has no free summand , then it can be defined via a minimal resolution?

Published on 29 Mar 2026 - 13:23

143

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Exercise 6.6 in Eisenbud's Commutative Algebra on the Family of Projective Plane Curves of Degree d

Published on 27 Mar 2026 - 20:21

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Difference between Modules and Vector Spaces

Proof Verification: $R[S]$ is a projective $R-$module (S is an arbitrary nonempty set)

Extracting Rank from a module isomorphism over a PID

Prove $(X,Y) \subset \mathbb{C}[X,Y]$ is not free as $\mathbb{C}[X,Y]$-module using two isomorphisms

Every projective module is a direct summand of free module.

Smallest direct summand containing a submodule

Lazard theorem, one direction

Prove $M$ is not free

Subgroups of $\mathbb{Z} \times \mathbb{Z}$ of index $p$ and $pq$

Isomorphism of vector spaces over the quotient of a ring

Universal splitting algebra of a monic polynomial over a field is a field?

About condition of homomorphism between $\mathbb{Z}[G]$-modules (free as $\mathbb{Z}$-module) factors through free $\mathbb{Z}[G]$-module

Consider $R=M_{n}(k)$ which $k$ is a field. Properties of $M$ as an $R$-Module.

If a module is second syzygy and has no free summand , then it can be defined via a minimal resolution?

Exercise 6.6 in Eisenbud's Commutative Algebra on the Family of Projective Plane Curves of Degree d

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