Article
| Title: | Projectively coresolved Gorenstein flat modules over trivial ring extensions (English) |
| Author: | Wang, Zhanping |
| Author: | Jin, Yuanhui |
| Author: | He, Jianyuan |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 445-460 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R\ltimes M$ be a trivial extension of a ring $R$ by an $R$-$R$-bimodule $M$. Sufficient and necessary conditions are established for projectively coresolved Gorenstein flat (PGF, for short) modules over $R\ltimes M$. More pecisely, it is proved that $(X, \alpha )$ is a PGF left \hbox {$R\ltimes M$-module} if and only if ${\rm Coker}(\alpha )$ is a PGF left $R$-module and the sequence $M\otimes _{R}M\otimes _{R}X \overset {M\otimes \alpha } \to \longrightarrow M\otimes _{R}X \overset {\alpha } \to \longrightarrow X$ is exact under some assumptions on $M$. As applications, it is characterized PGF modules over Morita rings with zero bimodule homomorphisms. (English) |
| Keyword: | PGF module |
| Keyword: | trivial ring extension |
| Keyword: | Morita ring |
| MSC: | 16D40 |
| MSC: | 16D50 |
| MSC: | 16E05 |
| DOI: | 10.21136/CMJ.2025.0505-23 |
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| Date available: | 2025-05-20T11:43:58Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152952 |
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