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Local Group Rings

Published online by Cambridge University Press:  20 November 2018

W. K. Nicholson
W. K. Nicholson*
Affiliation:
University of Calgary, Calgary, Alberta
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The purpose of this note is to generalize a result of Gulliksen, Ribenboim and Viswanathan which characterized local group rings when both the ring and the group are commutative.

We assume throughout that all rings are associative with identity. If R is a ring we call R local if R/J(R) is a division ring where J(R) denotes the Jacobson radical of R. It is well known that R is local if and only if each element of R\J(R) is a unit. We need the following.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 137 - 138
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Amitsur, S. A., On the semi-simplicity of group algebras, Michigan Math. J. 6 (1959), 251-253.Google Scholar
2. Connell, I. G., On the group ring, Canad. J. Math. 15 (1962), 650-685.Google Scholar
3. Gulliksen, T., Ribenboim, P. and Viswanathan, T. M., An elementary note on group rings, Crelles J. B 242 (1970), 148-162.Google Scholar