Modules whose maximal submodules have \(\tau\)-supplements
Let \(R\) be a ring and \(\tau\) be a preradical for the category of left \(R\)-modules. In this paper, we study on modules whose maximal submodules have \(\tau\)-supplements. We give some characterizations of these modules in terms their certain submodules, so called \(\tau\)-local submodules. For...
Saved in:
| Date: | 2018 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/646 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543036272541696 |
|---|---|
| author | Buyukasık, Engin |
| author_facet | Buyukasık, Engin |
| author_sort | Buyukasık, Engin |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:17:05Z |
| description | Let \(R\) be a ring and \(\tau\) be a preradical for the category of left \(R\)-modules. In this paper, we study on modules whose maximal submodules have \(\tau\)-supplements. We give some characterizations of these modules in terms their certain submodules, so called \(\tau\)-local submodules. For some certain preradicals \(\tau\), i.e. \(\tau=\delta\) and idempotent \(\tau\), we prove that every maximal submodule of \(M\) has a \(\tau\)-supplement if and only if every cofinite submodule of \(M\) has a \(\tau\)-supplement. For a radical \(\tau\) on \(\operatorname{R-Mod}\), we prove that, for every \(R\)-module every submodule is a \(\tau\)-supplement if and only if \(R/\tau(R)\) is semisimple and \(\tau\) is hereditary. |
| first_indexed | 2025-12-02T15:40:32Z |
| format | Article |
| id | admjournalluguniveduua-article-646 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:32Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6462018-04-04T09:17:05Z Modules whose maximal submodules have \(\tau\)-supplements Buyukasık, Engin preradical, \(\tau\)-supplement, \(\tau\)-local 16D10, 16N80 Let \(R\) be a ring and \(\tau\) be a preradical for the category of left \(R\)-modules. In this paper, we study on modules whose maximal submodules have \(\tau\)-supplements. We give some characterizations of these modules in terms their certain submodules, so called \(\tau\)-local submodules. For some certain preradicals \(\tau\), i.e. \(\tau=\delta\) and idempotent \(\tau\), we prove that every maximal submodule of \(M\) has a \(\tau\)-supplement if and only if every cofinite submodule of \(M\) has a \(\tau\)-supplement. For a radical \(\tau\) on \(\operatorname{R-Mod}\), we prove that, for every \(R\)-module every submodule is a \(\tau\)-supplement if and only if \(R/\tau(R)\) is semisimple and \(\tau\) is hereditary. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/646 Algebra and Discrete Mathematics; Vol 10, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/646/180 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | preradical \(\tau\)-supplement \(\tau\)-local 16D10 16N80 Buyukasık, Engin Modules whose maximal submodules have \(\tau\)-supplements |
| title | Modules whose maximal submodules have \(\tau\)-supplements |
| title_full | Modules whose maximal submodules have \(\tau\)-supplements |
| title_fullStr | Modules whose maximal submodules have \(\tau\)-supplements |
| title_full_unstemmed | Modules whose maximal submodules have \(\tau\)-supplements |
| title_short | Modules whose maximal submodules have \(\tau\)-supplements |
| title_sort | modules whose maximal submodules have \(\tau\)-supplements |
| topic | preradical \(\tau\)-supplement \(\tau\)-local 16D10 16N80 |
| topic_facet | preradical \(\tau\)-supplement \(\tau\)-local 16D10 16N80 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/646 |
| work_keys_str_mv | AT buyukasıkengin moduleswhosemaximalsubmoduleshavetausupplements |