2-clean rings

2006/10/30 by Zhou Wang, Jianlong Chen, Wang, Zhou +1
Mathematics · #16D40 #16D70 #16S50 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16D40 #msc:16D70 #msc:16S50

paper · pdf · doi:10.48550/arxiv.math/0610918

11 pages

arxiv created 2006/10/30 · arxiv updated 2009/12/01

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 RC_n is considered where R is a local ring. \vskip 0.5cm \bf Key words: 2-clean rings, 2-good rings, free modules, row and column-finite matrix rings, group rings.

Related

• Strong cleanness of the 2× 2 matrix ring over a general local ring
• Rings over which every matrix is the sum of two idempotents and a nilpotent
• Nil-good and nil-good clean matrix rings
• The strong P-cleanness over rings
• r-clean rings