Article
| Title: | Some results on quasi-t-dual Baer modules (English) |
| Author: | Tribak, Rachid |
| Author: | Talebi, Yahya |
| Author: | Hosseinpour, Mehrab |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 411-427 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a ring and let $M$ be an $R$-module with $S=\rm{End}_R(M)$. Consider the preradical ${\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}$ for the category of right $R$-modules Mod-$R$ introduced by Y. Talebi and N. Vanaja in 2002 and defined by ${\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}(M) = \bigcap \{U\leq M\colon M/U$ is small in its injective hull$\}$. The module $M$ is called quasi-t-dual Baer if $\sum_{\varphi \in \mathfrak{I}} \varphi({{\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}}^2(M))$ is a direct summand of $M$ for every two-sided ideal $\mathfrak{I}$ of $S$, where ${{\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}}^2(M) = {{\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}} ({{\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}}(M))$. In this paper, we show that $M$ is quasi-t-dual Baer if and only if ${{\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}}^2(M) $ is a direct summand of $M$ and ${\mkern 1.5mu\overline{\mkern-3.5mu Z \mkern-.5mu}\mkern 1.5mu}^2(M)$ is a quasi-dual Baer module. It is also shown that any direct summand of a quasi-t-dual Baer module inherits the property. The last part of the paper is devoted to the comparison of the notions of quasi-dual Baer modules and quasi-t-dual Baer modules. Also, right quasi-t-dual Baer rings are investigated. (English) |
| Keyword: | fully invariant submodule |
| Keyword: | quasi-dual Baer module |
| Keyword: | quasi-dual Baer ring |
| Keyword: | quasi-t-dual Baer module |
| Keyword: | quasi-t-dual Baer ring |
| MSC: | 16D10 |
| MSC: | 16D80 |
| DOI: | 10.14712/1213-7243.2024.008 |
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| Date available: | 2024-11-05T11:44:36Z |
| Last updated: | 2024-11-05 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152621 |
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