Maximal quotient rings of group rings

Edward William Formanek

Vol. 53 (1974), No. 1, 109–116

DOI: 10.2140/pjm.1974.53.109

Abstract

Let F[G] be the group ring of a group G over a field F, and Δ the subgroup of G consisting of those elements with only finitely many conjugates. Let Q(R) denote the maximal (Utumi) quotient ring of a ring R. This paper proves: (1) If H is a subnormaI subgroup of G,Q(F[H]) is naturally embedded as a subring of Q(F[G]). (2) Q(F[Δ]) contains the center of Q(F[G]). (3) If F[G] is semiprime with center C, Q(C) is the center of Q(F[G]). These results are analogues of theorems of M. Smith and D.S. Passman for the classical (Ore) quotient ring.

Mathematical Subject Classification

Primary: 16A08

Milestones

Received: 13 June 1973

Published: 1 July 1974