Torsion-free soluble groups, completions, and the zero divisor conjecture

W.W. Crawley-Boevey, P.H. Khopholler, P.A. Linnell
1988 Journal of Pure and Applied Algebra  
This paper contains two results which bear upon the zero-divisor conjecture for group rings. The first, proved using commutative algebra, asserts that a finitely generated torsion-free metabelian-by-finite group has many torsion-free quotients of finite rank. The second result concerns the completion of the group algebra kG at its augmentation ideal when G is a polycyclic pro-/> group and k is an algebraically closed field of characteristic p>O. For example, if G is torsionfree it is shown that
more » ... this completion is a domain. These two results imply that if G is a torsion-free soluble group of derived length at most three, and K is a field of characteristic zero, then KG is a domain. 1x1 W. W. Crowley-Boevey el 01.
doi:10.1016/0022-4049(88)90029-1 fatcat:4whekt5qg5e7tijbxgcelzcg4y