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1. CMB Online first

Ivanov, S. V.; Mikhailov, Roman
 On Zero-divisors in Group Rings of Groups with Torsion Nontrivial pairs of zero-divisors in group rings are introduced and discussed. A problem on the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of odd exponent $n \gg 1$ is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion. Keywords:Burnside groups, free products of groups, group rings, zero-divisorsCategories:20C07, 20E06, 20F05, , 20F50

2. CMB 2009 (vol 52 pp. 145)

Wang, Z.; Chen, J. L.
 $2$-Clean Rings 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 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 $\omega\times \omega$ 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. Keywords:$2$-clean rings, $2$-good rings, free modules, row and column-finite matrix rings, group ringsCategories:16D70, 16D40, 16S50