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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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/178 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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