Antisymmetric elements in group rings II

Let R be a commutative ring, G a group and RG its group ring. Let ' : RG → RG denote the R-linear extension of an involution ' defined on G. An element x in RG is said to be '- antisymmetric if '(x) = −x. A characterization is given of when the '-antisymmetric elements of RG commute. This is a completion of earlier work.Research supported by Onderzoeksraad of Vrije Universiteit Brussel, Fonds voor Wetenschappelijk Onderzoek (Vlaanderen), Flemish-Polish bilateral agreement BIL 01/31, FAPEMIG and CNPq. Proc. 300243/79-0(RN) of Brazil, D.G.I. of Spain and Fundación Séneca of Región de Murcia