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On the group ring of a finite abelian group

Published online by Cambridge University Press:  17 April 2009

Raymond G. Ayoub  and
Christine Ayoub
Raymond G. Ayoub
Affiliation:
Pennsylvania State University, University Park, Pennsylvania, USA.
Christine Ayoub
Affiliation:
Pennsylvania State University, University Park, Pennsylvania, USA.
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Abstract

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The group ring of a finite abelian group G over the field of rational numbers Q and over the rational integers Z is studied. A new proof of the fact that the group ring QG is a direct sum of cyclotomic fields is given – without use of the Maschke and Wedderburn theorems; it is shown that the projections of QG onto these fields are determined by the inequivalent characters of G. It is proved that the group of units of ZG is a direct product of a finite group and a free abelian group F and the rank of F is determined. A formula for the orthogonal idempotents of QG is found.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 2 , August 1969 , pp. 245 - 261
Copyright
Copyright © Australian Mathematical Society 1969

References

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