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Almost nilpotent gamma rings

Published online by Cambridge University Press:  17 April 2009

G.L. Booth  and
N.J. Groenewald
G.L. Booth
Affiliation:
Department of MathematicsUniversity of ZululandPrivate Bag X1001Kwadlangezwa 3886South Africa
N.J. Groenewald
Affiliation:
Department of MathematicsUniversity of Port ElizabethP.O. Box 1600Port Elizabeth 6000South Africa
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Abstract

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In this paper we introduce the concept of almost nilpotence for Γ-rings, similar to the corresponding concept for rings, as defined by Van Leeuwen and Heyman. An almost mlpotent radical property Α0 is introduced for Γ-rings, and shown to be supernilpotent. If M is a Γ-ring with left and right operator rings L and R respectively, then Α(L)+ = Α0(M) = Α(R)*, where Α(−) denotes the almost nilpotent radical of a ring. If M is a Γ-ring and m, n are positive integers, then Α0(Mm, n) is the almost nilpotent radical of the Γn, m-ring Mm, n.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 237 - 244
Copyright
Copyright © Australian Mathematical Society 1990

References

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