Generalized \(\oplus\)-supplemented modules
Let \(R\) be a ring and \(M\) be a left \(R\)-module. \(M\) is called generalized \(\oplus\)- supplemented if every submodule of \(M\) has a generalized supplement that is a direct summand of \(M\). In this paper we give various properties of such modules. We show that any finite direct sum of gene...
Saved in:
| Date: | 2018 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/647 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543354508017664 |
|---|---|
| author | Calısıcı, Hamza Turkmen, Ergul |
| author_facet | Calısıcı, Hamza Turkmen, Ergul |
| author_sort | Calısıcı, Hamza |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:17:05Z |
| description | Let \(R\) be a ring and \(M\) be a left \(R\)-module. \(M\) is called generalized \(\oplus\)- supplemented if every submodule of \(M\) has a generalized supplement that is a direct summand of \(M\). In this paper we give various properties of such modules. We show that any finite direct sum of generalized \(\oplus\)-supplemented modules is generalized \(\oplus\)-supplemented. If \(M\) is a generalized \(\oplus\)-supplemented module with \((D3)\), then every direct summand of \(M\) is generalized \(\oplus\)-supplemented. We also give some properties of generalized cover. |
| first_indexed | 2026-02-08T07:57:58Z |
| format | Article |
| id | admjournalluguniveduua-article-647 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:58Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6472018-04-04T09:17:05Z Generalized \(\oplus\)-supplemented modules Calısıcı, Hamza Turkmen, Ergul generalized cover, generalized supplemented module, \(\oplus\)-supplemented module, generalized \(\oplus\)-supplemented module 16D10,16D99 Let \(R\) be a ring and \(M\) be a left \(R\)-module. \(M\) is called generalized \(\oplus\)- supplemented if every submodule of \(M\) has a generalized supplement that is a direct summand of \(M\). In this paper we give various properties of such modules. We show that any finite direct sum of generalized \(\oplus\)-supplemented modules is generalized \(\oplus\)-supplemented. If \(M\) is a generalized \(\oplus\)-supplemented module with \((D3)\), then every direct summand of \(M\) is generalized \(\oplus\)-supplemented. We also give some properties of generalized cover. 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/647 Algebra and Discrete Mathematics; Vol 10, No 2 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/647/181 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | generalized cover generalized supplemented module \(\oplus\)-supplemented module generalized \(\oplus\)-supplemented module 16D10,16D99 Calısıcı, Hamza Turkmen, Ergul Generalized \(\oplus\)-supplemented modules |
| title | Generalized \(\oplus\)-supplemented modules |
| title_full | Generalized \(\oplus\)-supplemented modules |
| title_fullStr | Generalized \(\oplus\)-supplemented modules |
| title_full_unstemmed | Generalized \(\oplus\)-supplemented modules |
| title_short | Generalized \(\oplus\)-supplemented modules |
| title_sort | generalized \(\oplus\)-supplemented modules |
| topic | generalized cover generalized supplemented module \(\oplus\)-supplemented module generalized \(\oplus\)-supplemented module 16D10,16D99 |
| topic_facet | generalized cover generalized supplemented module \(\oplus\)-supplemented module generalized \(\oplus\)-supplemented module 16D10,16D99 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/647 |
| work_keys_str_mv | AT calısıcıhamza generalizedoplussupplementedmodules AT turkmenergul generalizedoplussupplementedmodules |