Symmetric modules over their endomorphism rings
Let \(R\) be an arbitrary ring with identity and \(M\) a right\(R\)-module with \(S=End_R(M)\). In this paper, we study right\(R\)-modules \(M\) having the property for \(f,g \in End_R(M)\) andfor \(m\in M\), the condition \(fgm = 0\) implies \(gfm = 0\). We provethat some results of symmetric rings...
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| Date: | 2015 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2015
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/71 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543266535636992 |
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| author | Ungor, Burcu Kurtulmaz, Yosum Halicioglu, Sait Harmanci, Abdullah |
| author_facet | Ungor, Burcu Kurtulmaz, Yosum Halicioglu, Sait Harmanci, Abdullah |
| author_sort | Ungor, Burcu |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2015-09-28T11:22:08Z |
| description | Let \(R\) be an arbitrary ring with identity and \(M\) a right\(R\)-module with \(S=End_R(M)\). In this paper, we study right\(R\)-modules \(M\) having the property for \(f,g \in End_R(M)\) andfor \(m\in M\), the condition \(fgm = 0\) implies \(gfm = 0\). We provethat some results of symmetric rings can be extended to symmetricmodules for this general setting. |
| first_indexed | 2025-12-02T15:32:15Z |
| format | Article |
| id | admjournalluguniveduua-article-71 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:32:15Z |
| publishDate | 2015 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-712015-09-28T11:22:08Z Symmetric modules over their endomorphism rings Ungor, Burcu Kurtulmaz, Yosum Halicioglu, Sait Harmanci, Abdullah symmetric modules, reduced modules, rigid modules, semicommutative modules, abelian modules, Rickart modules, principally projective modules 13C99, 16D80 Let \(R\) be an arbitrary ring with identity and \(M\) a right\(R\)-module with \(S=End_R(M)\). In this paper, we study right\(R\)-modules \(M\) having the property for \(f,g \in End_R(M)\) andfor \(m\in M\), the condition \(fgm = 0\) implies \(gfm = 0\). We provethat some results of symmetric rings can be extended to symmetricmodules for this general setting. Lugansk National Taras Shevchenko University 2015-09-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/71 Algebra and Discrete Mathematics; Vol 19, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/71/20 Copyright (c) 2015 Algebra and Discrete Mathematics |
| spellingShingle | symmetric modules reduced modules rigid modules semicommutative modules abelian modules Rickart modules principally projective modules 13C99 16D80 Ungor, Burcu Kurtulmaz, Yosum Halicioglu, Sait Harmanci, Abdullah Symmetric modules over their endomorphism rings |
| title | Symmetric modules over their endomorphism rings |
| title_full | Symmetric modules over their endomorphism rings |
| title_fullStr | Symmetric modules over their endomorphism rings |
| title_full_unstemmed | Symmetric modules over their endomorphism rings |
| title_short | Symmetric modules over their endomorphism rings |
| title_sort | symmetric modules over their endomorphism rings |
| topic | symmetric modules reduced modules rigid modules semicommutative modules abelian modules Rickart modules principally projective modules 13C99 16D80 |
| topic_facet | symmetric modules reduced modules rigid modules semicommutative modules abelian modules Rickart modules principally projective modules 13C99 16D80 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/71 |
| work_keys_str_mv | AT ungorburcu symmetricmodulesovertheirendomorphismrings AT kurtulmazyosum symmetricmodulesovertheirendomorphismrings AT halicioglusait symmetricmodulesovertheirendomorphismrings AT harmanciabdullah symmetricmodulesovertheirendomorphismrings |