Peter DANCHEV

A generalization of $\pi$-regular rings

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Öz We introduce the class of so-called { regularly nil clean rings} and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as exchange rings, Utumi rings etc. These rings of ours naturally generalize the long-known classes of $\pi$-regular and strongly $\pi$-regular rings. We show that the regular nil cleanness possesses a symmetrization which extends the corresponding one for strong $\pi$-regularity that was visualized by Dischinger \cite{Dis}. Likewise, our achieved results substantially improve on establishments presented in two recent papers by Danchev and \v{S}ter \cite{DS} and Danchev \cite{Da}.

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