• Uniquely Clean Idempotent 2×2 Matrices Over Integral Domains

Abstract

Let R be a ring with identity. An element of R is said to be clean if it is the sum of a unit and an idempotent and it is uniquely clean if this representation is unique. It is well known that central idempotents in any ring are uniquely clean ([2]). In this paper it has been shown that if R is an Integral Domain then the central idempotents are the only uniquely clean idempotents in .