Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909980720889856 |
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| author | Zhang, Xiaolei Qi, Wei |
| author_facet | Zhang, Xiaolei Qi, Wei |
| contents | In this paper, we give some new characterizations of $u$-$S$-Noetherian rings and $u$-$S$-coherent rings in terms of uniform $S$-version of injective precovers, flat preenvelopes and absolutely pure modules, respectively. Moreover, we give a negative answer to a question proposed by Bouziri [3]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings Zhang, Xiaolei Qi, Wei Commutative Algebra In this paper, we give some new characterizations of $u$-$S$-Noetherian rings and $u$-$S$-coherent rings in terms of uniform $S$-version of injective precovers, flat preenvelopes and absolutely pure modules, respectively. Moreover, we give a negative answer to a question proposed by Bouziri [3]. |
| title | Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2508.21400 |