2-Clean Rings *

Z. Wang and J.L. Chen

Abstract. A 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 ring 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.
Key words: 2-clean rings, 2-good rings, free modules, row and column- finite matrix rings, group rings.
AMS Subject Classification: 16D70, 16D40, 16S50.

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