2-Clean Rings

Abstract

AbstractA ring R is said to be n-clean if every element can be written as a sum of an idempotent and n units. The class of these rings contains clean rings and n-good rings in which each element is a sum of n units. In this paper, we show that for any ring R, the endomorphism ring of a free R-module of rank at least 2 is 2-clean and that the ring B(R) of all ω × ω row and column-finite matrices over any ring R is 2-clean. Finally, the group ring RCn is considered where R is a local ring.