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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| Datum: | 2018 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | 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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Algebra and Discrete Mathematics| _version_ | 1856543423994003456 |
|---|---|
| author | Keskin Tütüncü, Derya Orhan Ertas, Nil Tribak, Rachid |
| author_facet | Keskin Tütüncü, Derya Orhan Ertas, Nil Tribak, Rachid |
| author_sort | Keskin Tütüncü, Derya |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-07-24T22:56:15Z |
| 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. |
| first_indexed | 2025-12-02T15:42:20Z |
| format | Article |
| id | admjournalluguniveduua-article-178 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:42:20Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | On dual Rickart modules and weak dual Rickart modules |
| title_sort | on dual rickart modules and weak dual rickart modules |
| topic | dual Rickart modules weak dual Rickart modules weak Rickart rings V-rings Primary 16D10 Secondary 16D80 |
| topic_facet | dual Rickart modules weak dual Rickart modules weak Rickart rings V-rings Primary 16D10 Secondary 16D80 |
| 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 |