Glasgow Mathematical Journal

Table of Contents - 1997 - Volume 39, Issue 01  

Research Article

Semigroup identities on units of integral group rings

Michael A. Dokuchaeva1 and Jairo Z. Gonçalvesa1†

a1 Instituto de Matemática e Estatistica, Universidade de Sāo Paulo, CP 66281-AG Cid. de Sāo Paulo, CEP 05389-970 Sāo Paulo-Brazil, dokucha@ime.usp.br, jzg@ime.usp.br

Abstract

Let U(RG) be the group of units of a group ring RG over a commutative ring R with 1. We say that a group is an SIT-group if it is an extension of a group which satisfies a semigroup identity by a torsion group. It is a consequence of the main result that if G is torsion and R = Z, then U(RG) is an SIT-group if and only if G is either abelian or a Hamiltonian 2-group. If R is a local ring of characteristic 0 only the first alternative can occur.

(Received August 16 1994)

Footnotes

† The first author was supported by NSERC-Canada and the second by CNPq-Brazil.