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On Reversible Group Rings

Published online by Cambridge University Press:  17 April 2009

Yuanlin Li
Affiliation:
Department of MathematicsBrock UniversitySt. Catharines, OntarioCanadaL2S 3A1 e-mail: yli@brocku.ca
Howard E. Bell
Affiliation:
Department of MathematicsBrock UniversitySt. Catharines, OntarioCanadaL2S 3A1 e-mail: hbell@brocku.ca
Colin Phipps
Affiliation:
Department of MathematicsBrock UniversitySt. Catharines, OntarioCanadaL2S 3A1 e-mail: cp03nx@brocku.ca
Corresponding
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Extract

Let G be an arbitrary finite group, R be a finite associative ring with identity and RG be the group ring. We show that ℤ2Q8 is the minimal reversible group ring which is not symmetric, and we also characterise the finite rings R for which RQ8 is reversible. The first result extends a result of Gutan and Kisielewicz which shows that ℤ2Q8 is the minimal reversible group algebra over a field which is not symmetric, and it answers a question raised by Marks for the group ring case.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

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