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Artinian quotient rings of group rings

Published online by Cambridge University Press:  09 April 2009

Ian Hughes
Ian Hughes
Affiliation:
Department of Mathematics Queen's UniversityKingston, Ontario, Canada
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Smith [6, Theorem 2.18] proved that if A is a ring which has a right artinian right quotient ring and G is a poly- (cyclic-or-finite) group, then the group ring AG has a right artinian right quotient ring. We give here a different proof (and a generalization) of this result using methods developed by Jategaonkar [3,4]. THEOREM. Let A be a ring which has a right artinian right quotient ring, and let G be a group which has a (transfinite) ascending normal series with each factor either finite or cyclic, but only a finite number of finite factors. Then AG has a right artinian right quotient ring.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 3 , November 1973 , pp. 379 - 384
Copyright
Copyright © Australian Mathematical Society 1973

References

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