Article
| Title: | On $S$-injective and $S$-FP-injective (pre)covers (English) |
| Author: | Bennis, Driss |
| Author: | Bouziri, Ayoub |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 905-915 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring and $S$ a multiplicative subset of $R$. This paper is a sequel to previous works, where we established some module-theoretic characterizations of $S$-Noetherian and $S$-coherent rings. We show that, under certain conditions, a ring $R$ is \hbox {$S$-Noetherian} (or $S$-coherent) if and only if the class of all $S$-injective (or $S$-FP-injective) $R$-modules is (pre)covering. These results provide the $S$-counterpart of Enochs's (or Pinzon, Dai, and Ding's) characterizations for Noetherian (or coherent) rings using the notion of (pre)covering. (English) |
| Keyword: | $S$-Noetherian ring |
| Keyword: | $S$-coherent ring |
| Keyword: | $S$-injective module |
| Keyword: | $S$-FP-injective module |
| MSC: | 13C13 |
| MSC: | 13E15 |
| MSC: | 16D70 |
| DOI: | 10.21136/CMJ.2026.0427-25 |
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| Date available: | 2026-09-11T13:13:46Z |
| Last updated: | 2026-09-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153733 |
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