A new characterization of a strongly clean ring is given. And it is proven that if R is a strongly clean ring, then eRe is a strongly clean ring for e 2 = e ∈ R, which answers a question of Nicholson (1999 Nicholson , W. K. ( 1999 ). Strongly clean rings and Fitting's lemma . Comm. Algebra 27 ( 8 ): 3583 – 3592 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in the affirmative.
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Weixing Chen (2006) studied this question.
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