zbMATH — the first resource for mathematics

Projective modules, zero divisors, and Noetherian group algebras. (English) Zbl 0542.16010
Algebra and its applications, Int. Symp., New Delhi 1981, Lect. Notes Pure Appl. Math. 91, 169-185 (1984).
[For the entire collection see Zbl 0534.00007.]
This paper gives an exposition of the proof of the zero-divisor conjecture for group rings of polycyclic-by-finite groups. This was proved by the reviewer and D. R. Farkas in characteristic 0 [J. Algebra 42, 192-198 (1976; Zbl 0355.16004)] and in characteristic \(p>0\) by G. H. Cliff [Can. J. Math. 32, 596-602 (1980; Zbl 0439.16011)]. The exposition follows the original proofs.
Reviewer: R.L.Snider
16S34 Group rings
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)