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Ring endomorphisms satisfying the central reversible property

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Abstract

A ring R is called reversible if for \(a, b \in R\), \(ab=0\) implies \(ba=0\). These rings play an important role in the study of noncommutative ring theory. Kafkas et al. (Algebra Discrete Math. 12 (2011) 72–84) generalized the notion of reversible rings to central reversible rings. In this paper, we extend the notion of central reversibility of rings to ring endomorphisms. We investigate various properties of these rings and answer relevant questions that arise naturally in the process of development of these rings, and as a consequence many new results related to central reversible rings are also obtained as corollaries to our results.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her valuable comments which helped to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Assam University, Silchar, 788 011, India

    Arnab Bhattacharjee & Uday Shankar Chakraborty

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  1. Arnab Bhattacharjee
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  2. Uday Shankar Chakraborty
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Correspondence to Uday Shankar Chakraborty.

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Communicating Editor: Mrinal Kanti Das

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Bhattacharjee, A., Chakraborty, U.S. Ring endomorphisms satisfying the central reversible property. Proc Math Sci 130, 12 (2020). https://doi.org/10.1007/s12044-019-0548-y

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  • DOI: https://doi.org/10.1007/s12044-019-0548-y

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