Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2018; 55(3): 913-920

Online first article February 28, 2018      Printed May 31, 2018

https://doi.org/10.4134/BKMS.b170384

Copyright © The Korean Mathematical Society.

Sums of tripotent and nilpotent matrices

Marjan Sheibani Abdolyousefi, Huanyin Chen

Women's University of Semnan (Farzanegan), Hangzhou Normal University

Abstract

Let $R$ be a 2-primal strongly 2-nil-clean ring. We prove that every square matrix over $R$ is the sum of a tripotent and a nilpotent matrices. The similar result for rings of bounded index is proved. We thereby provide a large class of rings over which every matrix is the sum of a tripotent and a nilpotent matrices.

Keywords: tripotent matrix, nilpotent matrix, strongly 2-nil-clean ring, 2-prime ring

MSC numbers: 16S34, 16U99, 16E50

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