Some classes of strongly clean rings

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.


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