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Nil and s-prime Ω-groups

Part of: Other generalizations of groups

Published online by Cambridge University Press:  09 April 2009

A. Buys  and
G. K. Gerber
A. Buys
Affiliation:
Department of Mathematics University of Port Elizabeth6000 Port Elizabeth Republic of, South Africa
G. K. Gerber
Affiliation:
Department of Mathematics University of Port Elizabeth6000 Port Elizabeth Republic of, South Africa
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Abstract

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The concepts nilpotent element, s-prime ideal and s-semi-prime ideal are defined for Ω-groups. The class {G|G is a nil Ω-group} is a Kurosh-Amitsur radical class. The nil radical of an Ω-group coincides with the intersection of all the s-prime ideals. Furthermore an ideal P of G is an s-semi-prime ideal if and only if G/P has no non-zero nil ideals.

MSC classification

Secondary: 20N99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 222 - 229
Copyright
Copyright © Australian Mathematical Society 1985

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