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Licensed Unlicensed Requires Authentication Published by De Gruyter March 12, 2009

Antisymmetric elements in group rings with an orientation morphism

O. Broche, E. Jespers and M. Ruiz
From the journal


Let R be a commutative ring, G a group and RG its group ring. Let φσ : RGRG denote the involution defined by φσrgg) = Σrgσ(g)g–1, where σ : G → {±1} is a group homomorphism (called an orientation morphism). An element x in RG is said to be antisymmetric if φσ(x) = –x. We give a full characterization of the groups G and its orientations for which the antisymmetric elements of RG commute.

Received: 2007-05-09
Accepted: 2007-09-24
Published Online: 2009-03-12
Published in Print: 2009-May

© de Gruyter 2009