Some remarks on injective envelopes on ring extensions
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916376772345856 |
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| author | Zhang, Xiaolei |
| author_facet | Zhang, Xiaolei |
| contents | Let $f:S\rightarrow R$ be a ring extension. We introduce and study the properties of $(R, S)_\star$-injective modules and the existences of $(R, S)_\star$-injective envelopes. Besides, we show that every $R$-module has an $(R, S)$-injective envelope when $S$ is a pure-semisimple ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks on injective envelopes on ring extensions Zhang, Xiaolei Rings and Algebras Let $f:S\rightarrow R$ be a ring extension. We introduce and study the properties of $(R, S)_\star$-injective modules and the existences of $(R, S)_\star$-injective envelopes. Besides, we show that every $R$-module has an $(R, S)$-injective envelope when $S$ is a pure-semisimple ring. |
| title | Some remarks on injective envelopes on ring extensions |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2407.16146 |