Article
| Title: | On $w$-universal injective modules and their applications in commutative rings (English) |
| Author: | Zhou, Dechuan |
| Author: | Kim, Hwankoo |
| Author: | Zhao, Wei |
| Author: | Hu, Kui |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 915-932 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring and $w$ be the $w$-operation on $R$. We introduce the concept of $w$-universal injective modules and establish their fundamental properties. It is shown that the product of $E(R/{\frak m})$, where ${\frak m}$ ranges over maximal $w$-ideals of $R$, is a \hbox {$w$-universal} injective $w$-module over $R$, albeit not necessarily a universal injective \hbox {$R$-module}. As applications, we characterize $w$-IF rings and $w$-coherent rings using $w$-universal injective modules. Specifically, we demonstrate that $R$ is a $w$-IF ring if and only if $R$ is $w$-coherent and $E(R/{\frak m})$ is a flat $R$-module for every ${\frak m} \in w \text {-Max}(R)$. These results extend existing results and provide deeper insights into the structure of $w$-modules. (English) |
| Keyword: | $w$-universal injective |
| Keyword: | $w$-flat module |
| Keyword: | $w$-IF ring |
| Keyword: | $w$-coherent ring |
| MSC: | 13A15 |
| MSC: | 13C99 |
| DOI: | 10.21136/CMJ.2025.0503-24 |
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| Date available: | 2025-09-19T11:57:36Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153058 |
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