Strongly Clean Matrices in M2(Z): An Intrinsic Characterization

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. When R is a projective free ring, a characterization of strongly clean elements in has been given [7]. When R is a principal ideal domain (P.I.D.), towards such a characterization we take an approach which uses well known structure of idempotent matrices in . We use this to characterize non triangular strongly clean elements in in terms of their entries