Antisymmetric Elements in Group Rings II

Details Antisymmetric Elements in Group Rings II Antisymmetric Elements in Group Rings II

2008-01-29

arxiv.org/abs/0801.4451v1

Mathematics

Rings and Algebras

Scientific paper

Let $R$ be a commutative ring, $G$ a group and $RG$ its group ring. Let $\vp
: RG\to RG$ denote the $R$-linear extension of an involution $\vp$ defined on
$G$. An element $x$ in $RG$ is said to be $\vp$-antisymmetric if $\vp (x) =
-x$. A characterization is given of when the $\vp$-antisymmetric elements of
$RG$ commute. This is a completion of earlier work.

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