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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/2404.04610 |
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| _version_ | 1866913400707088384 |
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| author | Zhang, Xiaolei |
| author_facet | Zhang, Xiaolei |
| contents | Let $R$ be a ring and $S$ a multiplicative subset of $R$. In this note, we study the localization of $S$-injective modules and $u$-$S$-injective modules under $S$-Noetherian rings and $u$-$S$-Noetherian rings, respectively. The $u$-$S$-absolutely pure property is showed to be preserved under localizations over $S$-coherent rings. Besides, we give an example to show the difference between $S$-injective modules and $u$-$S$-injective modules, and some counter-examples to deny some questions proposed in \cite{B24}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the localization of generalized injective modules Zhang, Xiaolei Commutative Algebra Let $R$ be a ring and $S$ a multiplicative subset of $R$. In this note, we study the localization of $S$-injective modules and $u$-$S$-injective modules under $S$-Noetherian rings and $u$-$S$-Noetherian rings, respectively. The $u$-$S$-absolutely pure property is showed to be preserved under localizations over $S$-coherent rings. Besides, we give an example to show the difference between $S$-injective modules and $u$-$S$-injective modules, and some counter-examples to deny some questions proposed in \cite{B24}. |
| title | A note on the localization of generalized injective modules |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2404.04610 |