Some families of strongly clean rings

A ring R with identity is called strongly clean if every element of R is the sum of an idempotent and a unit that commute with each other. For a commutative local ring R and for an arbitrary integer n⩾2, the paper deals with the question whether the strongly clean property of Mn(R[[x]]), , and Mn(RC2) follows from the strongly clean property of Mn(R). This is ‘Yes’ if n=2 by a known result.