List questions from free-modules

Published on 06 May 2019 - 19:41

63

Views

Example of both finitely and infinitely generated free modules which are direct sum of two non free modules

Published on 08 May 2019 - 23:24

301

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Unique representation of zero in terms of the basis of a free module

Published on 09 May 2019 - 17:53

526

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The exact sequence of tensor product

Published on 10 May 2019 - 7:06

470

Views

Proof explanation: Every module is the quotient of free module

Published on 14 May 2019 - 1:14

479

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Is a finitely generated torsion-free R-module free over R if R is an integral domain?

Published on 17 May 2019 - 1:38

2k

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Pullback of locally free sheaves is locally free

Published on 25 Mar 2026 - 9:39

212

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Basis of a free module under module homomorphisms

Published on 22 May 2019 - 12:00

391

Views

Linear independence for modules over a zero ring

Published on 25 May 2019 - 11:33

113

Views

Modules $(K\otimes A)\otimes_{K}\left(K\otimes B\right)$ and $K\otimes(A\otimes B)$ isomorphic?

Published on 28 May 2019 - 9:42

902

Views

Determinant for a basis of a free module

Published on 09 Jun 2019 - 2:10

103

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$\Bbb R$-algebras of rank $1$

Published on 09 Jun 2019 - 22:43

97

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What do the finitely generated free $R$-modules look like?

Published on 11 Jun 2019 - 7:20

1.3k

Views

Why is every vector space free, but not every module?

Published on 27 Jun 2019 - 14:35

86

Views

I don't understand a step in the statement of the structure theorem of finitely generated modules over a PID

Published on 30 Jun 2019 - 20:10

List Question

Exact sequence construction

Example of both finitely and infinitely generated free modules which are direct sum of two non free modules

Unique representation of zero in terms of the basis of a free module

The exact sequence of tensor product

Proof explanation: Every module is the quotient of free module

Is a finitely generated torsion-free R-module free over R if R is an integral domain?

Pullback of locally free sheaves is locally free

Basis of a free module under module homomorphisms

Linear independence for modules over a zero ring

Modules $(K\otimes A)\otimes_{K}\left(K\otimes B\right)$ and $K\otimes(A\otimes B)$ isomorphic?

Determinant for a basis of a free module

$\Bbb R$-algebras of rank $1$

What do the finitely generated free $R$-modules look like?

Why is every vector space free, but not every module?

I don't understand a step in the statement of the structure theorem of finitely generated modules over a PID

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