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.
Huanyin Chen
Hangzhou Normal University
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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