Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39620131215Some classes of strongly clean rings10991115463ENH.ChenDepartment of Mathematics, Hangzhou Normal University, 310036, Hangzhou, ChinaJournal Article20110920A ring $R$ is a strongly clean ring if every element in <br />$R$ is the sum of an idempotent and a unit that commutate. We <br />construct some classes of strongly clean rings which have stable <br />range one. It is shown that such cleanness of $2 imes 2$ matrices <br />over commutative local rings is completely determined in terms of <br />solvability of quadratic equations.http://bims.iranjournals.ir/article_463_8ef77b04cf0305fbaba0af11fc78b480.pdf