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skew symmetric elements

Proceedings of the Edinburgh Mathematical Society (1)

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COMMUTATIVITY OF SKEW SYMMETRIC ELEMENTS IN GROUP RINGS
Osnel Broche Cristo, César Polcino Milies
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 1 / February 2007

Published online by Cambridge University Press:

09 February 2007, pp. 37-47
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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.