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Bull. Korean Math. Soc. 2021; 58(1): 47-58

Online first article December 28, 2020      Printed January 31, 2021

https://doi.org/10.4134/BKMS.b191064

Copyright © The Korean Mathematical Society.

Rings in which every element is a sum of a nilpotent and three tripotents

Jian Cui, Guoli Xia

Anhui Normal University; Memorial University of Newfoundland

Abstract

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In this article, we completely determine the rings for which every element is a sum of a nilpotent and three tripotents that commute with one another. We discuss this property for some extensions of rings, including group rings.

Keywords: Nilpotent, tripotent, sum of a nilpotent and three tripotents, Boolean ring, group ring

MSC numbers: Primary 16S34, 16U99

Supported by: This research was supported in part by Anhui Provincial Natural Science Foundation (No. 2008085MA06) and the Key Project of Anhui Education Committee (No. gxyqZD2019009).

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