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e-reversibility of rings via quasinilpotents

  • Handan Kose ORCID logo , Burcu Ungor ORCID logo EMAIL logo und Abdullah Harmanci ORCID logo
Veröffentlicht/Copyright: 29. Juni 2023
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Abstract

The reversible property of rings was introduced by Cohn and has important generalizations in noncommutative ring theory. In this paper, reversibility of rings is investigated in relation with quasinilpotents and idempotents, and our argument is spread out based on this. We call a ring R Qnil e-reversible if for any a , b R , being a b = 0 implies b a e R qnil for a prescribed idempotent e R , where R qnil denotes the set of all quasinilpotent elements of R. In the first, we determine the set R qnil for some classes of rings to investigate the structure of Qnil e-reversible rings. In the second, we use R qnil to define Qnil e-reversibility of rings. The notion of Qnil e-reversible ring is a proper generalization of that of e-semicommutative ring, Qnil-semicommutative ring, e-reversible ring and right (left) quasi-duo ring. We obtain some relations between a ring and its quotient rings in terms of Qnil e-reversibility. Applications via some ring extensions and examples illustrating our results are provided.

Acknowledgements

The authors would like to thank the referee for the valuable comments that improved the presentation of this paper.

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Received: 2023-02-05
Revised: 2023-03-14
Accepted: 2023-04-27
Published Online: 2023-06-29
Published in Print: 2023-12-01

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