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COMMUTATIVITY OF SKEW SYMMETRIC ELEMENTS IN GROUP RINGS

Published online by Cambridge University Press:  09 February 2007

Osnel Broche Cristo  and
César Polcino Milies
Osnel Broche Cristo
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, Brazil (osnelier@ime.usp.br; polcino@ime.usp.br)
César Polcino Milies
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970 São Paulo, Brazil (osnelier@ime.usp.br; polcino@ime.usp.br)
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Abstract

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Let $R$ be a commutative ring with unity and let $G$ be a group. The group ring $RG$ has a natural involution that maps each element $g\in G$ to its inverse. We denote by $RG^-$ the set of skew symmetric elements under this involution. We study necessary and sufficient conditions for $RG^-$ to be commutative.

Keywords

Primary 16U60Secondary 16W1020C07group ringskew symmetric elementsinvolution
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 1 , February 2007 , pp. 37 - 47
Copyright
Copyright © Edinburgh Mathematical Society 2007