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