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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
MSC:
16S34 Group rings
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)