Article
| Title: | Ding projective and Ding injective modules over trivial ring extensions (English) |
| Author: | Mao, Lixin |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 903-919 |
| 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 $M$ such that $M_{R}$, $_{R}M$, $(R,0)_{R\ltimes M}$ and $_{R\ltimes M}(R,0)$ have finite flat dimensions. We prove that $(X,\alpha )$ is a Ding projective left $R\ltimes M$-module if and only if the sequence $M\otimes _R M\otimes _R X\stackrel {M\otimes \alpha }\longrightarrow M\otimes _R X\stackrel {\alpha }\rightarrow X$ is exact and ${\rm coker}(\alpha )$ is a Ding projective left $R$-module. Analogously, we explicitly describe Ding injective $R\ltimes M$-modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms. (English) |
| Keyword: | trivial extension |
| Keyword: | Ding projective module |
| Keyword: | Ding injective module |
| MSC: | 16D40 |
| MSC: | 16D50 |
| MSC: | 16E05 |
| idZBL: | Zbl 07729544 |
| idMR: | MR4632864 |
| DOI: | 10.21136/CMJ.2023.0351-22 |
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| Date available: | 2023-08-11T14:28:09Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151781 |
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