Certain Units in M2(Z) which are Uniquely Clean

An element of a ring is clean if it is the sum of an idempotent and a unit and it is uniquely clean if this representation is unique. Characterization for clean elements in has been given [2]. Using this characterization some sufficient conditions have been given for certain units to be uniquely clean. Keywords: Uniquely clean, units, Diophantine equation. 2000 Mathematics Subject Classification: 16S50