On dual Rickart modules and weak dual Rickart modules
Let \(R\) be a ring. A right \(R\)-module \(M\) is called \(\mathrm{d}\)-Rickart if for every endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) is a direct summand of \(M\) and it is called \(\mathrm{wd}\)-Rickart if for every nonzero endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) contains a nonz...
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| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/178 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-1782018-07-24T22:56:15Z On dual Rickart modules and weak dual Rickart modules Keskin Tütüncü, Derya Orhan Ertas, Nil Tribak, Rachid dual Rickart modules, weak dual Rickart modules, weak Rickart rings, V-rings Primary 16D10; Secondary 16D80 Let \(R\) be a ring. A right \(R\)-module \(M\) is called \(\mathrm{d}\)-Rickart if for every endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) is a direct summand of \(M\) and it is called \(\mathrm{wd}\)-Rickart if for every nonzero endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) contains a nonzero direct summand of \(M\). We begin with some basic properties of \(\mathrm{(w)d}\)-Rickart modules. Then we study direct sums of \(\mathrm{(w)d}\)-Rickart modules and the class of rings for which every finitely generated module is \(\mathrm{(w)d}\)-Rickart. We conclude by some structure results. Lugansk National Taras Shevchenko University Scientific and Technological Research Council of Turkey 2018-07-25 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/178 Algebra and Discrete Mathematics; Vol 25, No 2 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/178/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/178/64 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-07-24T22:56:15Z |
| collection |
OJS |
| language |
English |
| topic |
dual Rickart modules weak dual Rickart modules weak Rickart rings V-rings Primary 16D10 Secondary 16D80 |
| spellingShingle |
dual Rickart modules weak dual Rickart modules weak Rickart rings V-rings Primary 16D10 Secondary 16D80 Keskin Tütüncü, Derya Orhan Ertas, Nil Tribak, Rachid On dual Rickart modules and weak dual Rickart modules |
| topic_facet |
dual Rickart modules weak dual Rickart modules weak Rickart rings V-rings Primary 16D10 Secondary 16D80 |
| format |
Article |
| author |
Keskin Tütüncü, Derya Orhan Ertas, Nil Tribak, Rachid |
| author_facet |
Keskin Tütüncü, Derya Orhan Ertas, Nil Tribak, Rachid |
| author_sort |
Keskin Tütüncü, Derya |
| title |
On dual Rickart modules and weak dual Rickart modules |
| title_short |
On dual Rickart modules and weak dual Rickart modules |
| title_full |
On dual Rickart modules and weak dual Rickart modules |
| title_fullStr |
On dual Rickart modules and weak dual Rickart modules |
| title_full_unstemmed |
On dual Rickart modules and weak dual Rickart modules |
| title_sort |
on dual rickart modules and weak dual rickart modules |
| description |
Let \(R\) be a ring. A right \(R\)-module \(M\) is called \(\mathrm{d}\)-Rickart if for every endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) is a direct summand of \(M\) and it is called \(\mathrm{wd}\)-Rickart if for every nonzero endomorphism \(\varphi\) of \(M\), \(\varphi(M)\) contains a nonzero direct summand of \(M\). We begin with some basic properties of \(\mathrm{(w)d}\)-Rickart modules. Then we study direct sums of \(\mathrm{(w)d}\)-Rickart modules and the class of rings for which every finitely generated module is \(\mathrm{(w)d}\)-Rickart. We conclude by some structure results. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/178 |
| work_keys_str_mv |
AT keskintutuncuderya ondualrickartmodulesandweakdualrickartmodules AT orhanertasnil ondualrickartmodulesandweakdualrickartmodules AT tribakrachid ondualrickartmodulesandweakdualrickartmodules |
| first_indexed |
2025-07-17T10:33:31Z |
| last_indexed |
2025-07-17T10:33:31Z |
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1837889918538350592 |