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On Group Rings

Published online by Cambridge University Press:  20 November 2018

D. B. Coleman
D. B. Coleman*
Affiliation:
University of Kentucky, Lexington, Kentucky
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Let R be a commutative ring with unity and let G be a group. The group ring RG is a free R-module having the elements of G as a basis, with multiplication induced by

The first theorem in this paper deals with idempotents in RG and improves a result of Connell. In the second section we consider the Jacobson radical of RG, and we prove a theorem about a class of algebras that includes RG when G is locally finite and R is an algebraically closed field of characteristic zero. The last theorem shows that if R is a field and G is a finite nilpotent group, then RG determines RP for every Sylow subgroup P of G, regardless of the characteristic of R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 2 , 01 April 1970 , pp. 249 - 254
Copyright
Copyright © Canadian Mathematical Society 1970

References

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