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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.19038 |
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| _version_ | 1866911969571766272 |
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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 |