Article
| Title: | Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings (English) |
| Author: | Zhang, Xiaolei |
| Author: | Qi, Wei |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 2 |
| Year: | 2026 |
| Pages: | 575-590 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We give some new characterizations of $u$-$S$-Noetherian rings and $u$-$S$-coherent rings in terms of uniform $S$-versions of injective precovers, flat preenvelopes and absolutely pure modules. Moreover, we give a negative answer to a question proposed by Bouziri. (English) |
| Keyword: | $u$-$S$-Noetherian ring |
| Keyword: | $u$-$S$-coherent ring |
| Keyword: | $u$-$S$-precover |
| Keyword: | $u$-$S$-absolutely pure module |
| Keyword: | $u$-$S$-preenvelope |
| MSC: | 13C11 |
| DOI: | 10.21136/CMJ.2026.0350-25 |
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| Date available: | 2026-05-22T11:22:30Z |
| Last updated: | 2026-05-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153650 |
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| Reference: | [3] Bouziri, A.: A note on $u$-$S$-Noetherian and $u$-$S$-coherent rings.(to appear) in J. Algebra Appl. 10.1142/S0219498826503020 |
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| Reference: | [14] Wang, F., Kim, H.: Foundations of Commutative Rings and Their Modules.Algebra and Applications 22. Springer, Singapore (2016). Zbl 1367.13001, MR 3587977, 10.1007/978-981-10-3337-7 |
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| Reference: | [16] Zhang, X.: Characterizing $S$-flat modules and $S$-von Neumann regular rings by uniformity.Bull. Korean Math. Soc. 59 (2022), 643-657. Zbl 1495.13019, MR 4432432, 10.4134/BKMS.b210291 |
| Reference: | [17] Zhang, X.: On uniformly $S$-absolutely pure modules.J. Korean Math. Soc. 60 (2023), 521-536. Zbl 1522.13018, MR 4581014, 10.4134/JKMS.j220055 |
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