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On algebraic rings

Published online by Cambridge University Press:  17 April 2009

M. Chacron
M. Chacron
Affiliation:
University of Windsor, Windsor, Ontario, and University of British Columbia, Vancouver, British Columbia.
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Abstract

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A ring R is π-regular (periodic) if for each element x of R there is n = n(x) SO that xn = xn.a.xn (xn = xn.1.xn) (a depending on x). Let R be an algebraic algebra over a commutative ring F With identity. In this paper we prove that if every π-regular image of the ring F is periodic, then R is periodic. This result applies in particular to the algebraic rings R (over the integers) considered by Drazin and to the algebraic algebras R over algebraically prime fields. It extends a result of Drazin on torsin-free algebraic rings and a generalization by this author of Drazin's result.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 385 - 389
Copyright
Copyright © Australian Mathematical Society 1969

References

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