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On uniformly strongly prime gamma rings

Published online by Cambridge University Press:  17 April 2009

G.L. Booth  and
N.J. Groenwald
G.L. Booth
Affiliation:
Department of Mathematics, University of Zululand, Private Bag X1001, 3886 Kwadlangezwa, Republic of South Africa
N.J. Groenwald
Affiliation:
Department of Mathematics, University of Port Elizabeth, P.O. Box 1600, 6000 Port Elizabeth, Republic of South Africa
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Abstract

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The concept of uniformly strongly prime (usp) is introduced for Γ-ring, and a usp radical τ(M) is defined for a Γ-ring M. If M has left and right unities, then τ(L)+ = τ(M) = τ(R)*, where L and R denote, respectively, the left and right operator rings of M, and τ(·) denotes the usp radical of a ring. If m, n are positive integers, then τ(Mmn) = (τ(M))mn, where Mmn is the matrix Γnm-ring. τ is shown to be a special radical in the variety of Γ-rings. τ1 is the upper radical determined by the class of usp Γ-rings of bound 1. τ ⊆ τ1, but the reverse inclusion does not hold in general. The place of τ and τ1 in the hierarchy of radicals for Γ-rings is shown.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 437 - 445
Copyright
Copyright © Australian Mathematical Society 1988

References

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