Strongly clean triangular matrix rings over local rings

Abstract: An element of a ring is called strongly clean if it can be written as the sum of a unit and an idempotent that commute. A ring is called strongly clean if each of its elements is strongly clean. In this paper, we investigate conditions on a local ring R that imply that is a strongly clean ring. It is shown that this is the case for commutative local rings R, as well as for a host of other classes of local rings. An example of a local ring A for which is not strongly clean is also given. [Copyright &y& Elsevier]