List questions from projective-module

Published on 12 Nov 2021 - 12:52

354

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Simple, Cyclic and Projective Modules

Published on 21 Nov 2021 - 2:07

122

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Simple objects with isomorphic projective covers

Published on 22 Nov 2021 - 16:18

2.5k

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Three ways to to prove that projective modules are flat

Published on 27 Mar 2026 - 4:16

37

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Let $R$ be an integral domain and let $X$ be a torsion module over $R$. Then $Tor_n(X,Y)$ is a torsion module for every $n≥0$.

Published on 06 Dec 2021 - 15:41

251

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Milnor Squares and Milnor Patching: Examples?

Published on 29 Mar 2026 - 14:55

120

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Being direct summand of free module implies having dual basis.

Published on 29 Mar 2026 - 19:27

168

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Show that the homology groups of different projective resolutions of the same R-module are isomorphic to one another

Published on 19 Dec 2021 - 16:56

240

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Non-finitely generated R-module

Published on 29 Mar 2026 - 22:25

207

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Projective resolution of $\mathbb{R}$ as an abelian group

Published on 12 Jan 2022 - 23:19

41

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Do images and kernels of invariant modules have the form $Mr$ and $\text{Ann}(r)$ respectively for some $r\in R$?

Published on 27 Mar 2026 - 23:14

42

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If $A$ is representation finite, then $\{pd(M)|pd(M)<\infty, M\in mod-A\}=max\{pd(M)|M$ indecomposable $\}$?

Published on 27 Feb 2026 - 22:09

33

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Are projections of non projective modules interesting?

Published on 04 Feb 2022 - 10:52

139

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Change of rings of scalars and projecivity?

Published on 25 Mar 2026 - 6:04

98

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When every finitely generated submodule of an R-module is cyclic?

Published on 27 Mar 2026 - 21:54

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Powers of the Auslander-Reiten translations

Simple, Cyclic and Projective Modules

Simple objects with isomorphic projective covers

Three ways to to prove that projective modules are flat

Let $R$ be an integral domain and let $X$ be a torsion module over $R$. Then $Tor_n(X,Y)$ is a torsion module for every $n≥0$.

Milnor Squares and Milnor Patching: Examples?

Being direct summand of free module implies having dual basis.

Show that the homology groups of different projective resolutions of the same R-module are isomorphic to one another

Non-finitely generated R-module

Projective resolution of $\mathbb{R}$ as an abelian group

Do images and kernels of invariant modules have the form $Mr$ and $\text{Ann}(r)$ respectively for some $r\in R$?

If $A$ is representation finite, then $\{pd(M)|pd(M)<\infty, M\in mod-A\}=max\{pd(M)|M$ indecomposable $\}$?

Are projections of non projective modules interesting?

Change of rings of scalars and projecivity?

When every finitely generated submodule of an R-module is cyclic?

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