Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2013; 50(1): 125-134

Printed January 31, 2013

https://doi.org/10.4134/BKMS.2013.50.1.125

Copyright © The Korean Mathematical Society.

On $2\times 2$ strongly clean matrices

Huanyin Chen

Hangzhou Normal University

Abstract

An element in a ring $R$ is strongly clean provided that it is the sum of an idempotent and a unit that commutate. In this note, several necessary and sufficient conditions under which a $2\times 2$ matrix over an integral domain is strongly clean are given. These show that strong cleanness over integral domains can be characterized by quadratic and Diophantine equations.

Keywords: strong cleanness, integral domain, $2\times 2$ matrix

MSC numbers: 15A13, 15B99, 16L99

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