# Some classes of strongly clean rings

Document Type : Research Paper

Author

Department of Mathematics, Hangzhou Normal University, 310036, Hangzhou, China

Abstract

A ring $R$ is a strongly clean ring if every element in
$R$ is the sum of an idempotent and a unit that commutate. We
construct some classes of strongly clean rings which have stable
range one. It is shown that such cleanness of $2 imes 2$ matrices
over commutative local rings is completely determined in terms of

Keywords

Main Subjects

### History

• Receive Date: 20 September 2011
• Revise Date: 23 October 2012
• Accept Date: 24 October 2012
• First Publish Date: 15 December 2013