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 Strongly clean matrix rings over noncommutative local rings Bull. Korean Math. Soc. 2009 Vol. 46, No. 1, 71-78 Printed January 1, 2009 Li Bingjun National University of Defense Technology Abstract : An element of a ring $R$ with identity is called strongly clean if it is the sum of an idempotent and a unit that commute, and $R$ is called strongly clean if every element of $R$ is strongly clean. Let $R$ be a noncommutative local ring, a criterion in terms of solvability of a simple quadratic equation in $R$ is obtained for $M_2(R)$ to be strongly clean. Keywords : strongly clean ring, matrix ring, local ring, similarity MSC numbers : 16U99, 16S50 Downloads: Full-text PDF