A note on n-clean group rings

Abstract

Let R be an associative ring with identity. An element x ∈ R is clean if x can be written as the sum of a unit and an idempotent in R. R is said to be clean if all of its elements are clean. Let n be a positive integer. An element x ∈ R is n-clean if it can be written as the sum of an idempotent and n units in R. R is said to be n-clean if all of its elements are n-clean. In this paper we obtain conditions which are necessary or sufficient for a group ring to be n-clean.