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On the radical of a group algebra over a commutative ring

Published online by Cambridge University Press:  18 May 2009

Gloria Potter
Gloria Potter
Affiliation:
State University of New York, Brockport, N.Y. 14420, U.S.A.
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Several people, including Wallace [4] and Passman [3], have studied the Jacobson radical of the group algebra F[G] where F is a field and G is a multiplicative group. In [4], for instance, Wallace proves that if G is an abelian group with Sylow p-subgroup P and if F is a field of characteristic p, then the Jacobson radical of F[G] equals the right ideal generated by the radical of F[P]. In this paper we shall study group algebras over arbitrary commutative rings. By a reduction to the case of a semi-simple commutative ring, we obtain Theorem 1 whose corollary contains a generalization of Wallace's theorem. Theorem 2, on the other hand, uses the first theorem to obtain results related to the main theorem of [3].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 1 , January 1977 , pp. 101 - 104
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

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