S-FP-injective modules
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914961199988736 |
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| author | Bennis, Driss Bouziri, Ayoub |
| author_facet | Bennis, Driss Bouziri, Ayoub |
| contents | Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective. Moreover, we establish, under certain conditions, counterparts of Matlis, Stenström and Cheatham-Stone's characterizations of S-coherent rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | S-FP-injective modules Bennis, Driss Bouziri, Ayoub Commutative Algebra Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective. Moreover, we establish, under certain conditions, counterparts of Matlis, Stenström and Cheatham-Stone's characterizations of S-coherent rings. |
| title | S-FP-injective modules |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2410.00167 |