List questions from free-modules

Published on 31 Oct 2019 - 6:07

137

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Dimension of a module

Published on 02 Nov 2019 - 1:30

100

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Prove that $(x_1, y_1)$ and $(x_2, y_2)$ form a basis of $\mathbb Z \oplus \mathbb Z$ iff $x_1y_2 - y_2x_1 = \pm 1$

Published on 02 Nov 2019 - 20:12

60

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Is the concept of a basis of a module over a ring meaningful if unity is not assumed?

Published on 03 Nov 2019 - 14:23

217

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Show that if $R/A$ is IBN then $R$ is IBN.

Published on 06 Nov 2019 - 20:20

394

Views

Over a PID, every submodule of a free module is free

Published on 13 Nov 2019 - 17:12

712

Views

Computing index of a submodule over the ring $\mathbb{Z}[\omega]$

Published on 24 Mar 2026 - 18:07

201

Views

Submodule of a free module over a principal ring

Published on 24 Nov 2019 - 12:04

107

Views

Lifting idempotent endomorphisms of the quotient of a projective module

Published on 30 Nov 2019 - 8:51

479

Views

Chain maps between projective complexes are nullhomotopic

Published on 01 Dec 2019 - 2:51

403

Views

Surjective Endomorphism of Finitely Generated Modules.

Published on 11 Dec 2019 - 8:10

123

Views

Prove that the $R$-module $I \bigoplus I$ is free on the generators $(2 ,1+\sqrt{-5})$ and $(1-\sqrt{-5},2)$.

Published on 16 Dec 2019 - 23:09

1k

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Sets with the same cardinality generates isomorphic free modules.

Published on 18 Dec 2019 - 2:16

113

Views

How can $\mathbb{R}/\mathbb{Z}$ be a free $\mathbb{R}$-module?

Published on 30 Dec 2019 - 18:49

1.6k

Views

R is a Noetherian ring, then every finitely generated R-module is finitely presented

Published on 07 Jan 2020 - 14:08

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Question regarding stably free module

Dimension of a module

Prove that $(x_1, y_1)$ and $(x_2, y_2)$ form a basis of $\mathbb Z \oplus \mathbb Z$ iff $x_1y_2 - y_2x_1 = \pm 1$

Is the concept of a basis of a module over a ring meaningful if unity is not assumed?

Show that if $R/A$ is IBN then $R$ is IBN.

Over a PID, every submodule of a free module is free

Computing index of a submodule over the ring $\mathbb{Z}[\omega]$

Submodule of a free module over a principal ring

Lifting idempotent endomorphisms of the quotient of a projective module

Chain maps between projective complexes are nullhomotopic

Surjective Endomorphism of Finitely Generated Modules.

Prove that the $R$-module $I \bigoplus I$ is free on the generators $(2 ,1+\sqrt{-5})$ and $(1-\sqrt{-5},2)$.

Sets with the same cardinality generates isomorphic free modules.

How can $\mathbb{R}/\mathbb{Z}$ be a free $\mathbb{R}$-module?

R is a Noetherian ring, then every finitely generated R-module is finitely presented

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