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Main Author: Hamid, Mohanad Farhan
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.19038
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author Hamid, Mohanad Farhan
author_facet Hamid, Mohanad Farhan
contents Suppose that $(\mathcal{F},\mathcal{M})$ is an injective structure of $R$-Mod such that the class $\mathcal{F}$ is closed for direct limits, then two modules in $\mathcal{M}$ are isomorphic if there are maps in $\mathcal{F}$ from each one of the modules into the other. Examples of module classes in such injective structures include (pure, coneat, and RD-) injective modules, as well as $τ$-injective modules for a hereditary torsion theory $τ$. Thus providing a generalization of a classical result of Bumby's and two recent ones by Macías-Díaz.
format Preprint
id arxiv_https___arxiv_org_abs_2407_19038
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Isomorphisms between injective modules
Hamid, Mohanad Farhan
Rings and Algebras
Suppose that $(\mathcal{F},\mathcal{M})$ is an injective structure of $R$-Mod such that the class $\mathcal{F}$ is closed for direct limits, then two modules in $\mathcal{M}$ are isomorphic if there are maps in $\mathcal{F}$ from each one of the modules into the other. Examples of module classes in such injective structures include (pure, coneat, and RD-) injective modules, as well as $τ$-injective modules for a hereditary torsion theory $τ$. Thus providing a generalization of a classical result of Bumby's and two recent ones by Macías-Díaz.
title Isomorphisms between injective modules
topic Rings and Algebras
url https://arxiv.org/abs/2407.19038