| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| idZBL:
|
Zbl 07953690 |
| idMR:
|
MR4813794 |
| DOI:
|
10.14712/1213-7243.2024.008 |
| . |
| Date available:
|
2024-11-05T11:44:36Z |
| Last updated:
|
2026-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152621 |
| . |
| Reference:
|
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