Document Type : Research Paper
Department of Mathematics, Hangzhou Normal University, 310036, Hangzhou, China
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
solvability of quadratic equations.