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On a problem of Szász

Published online by Cambridge University Press:  17 April 2009

Yasuyuki Hirano
Yasuyuki Hirano
Affiliation:
Department of MathematicsOkayama UniversityOkayama 700Japan
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Abstract

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Let R be a ring with centre Z. In this note, we prove the following: If the additive group Z+ of Z has finite group-theoretic index in R+, then R has an ideal I contained in Z such that R/I is a finite ring. This is a solution of a problem posed by F.A. Szász.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 363 - 364
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Szász, F.A., Radicals of Rings (John Wiley and Sons, Chichester, New York, Brisbane, Toronto, 1981).Google Scholar