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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

References

[1]Barnes, W. E., ‘On the Γ-rings of Nobusawa’, Pacific J. Math. 18 (1966), 411–422.Google Scholar
[2]Coppage, W. E. and Luh, J., ‘Radicals of Gamma rings’, J. Math. Soc. Japan 23 (1971), 40–52.CrossRefGoogle Scholar
[3]Groenewald, N. J., ‘Strongly semi-prime ideals in near-rings’, Chinese J. Math. 11 (1983), to appear.Google Scholar
[4]Higgins, P. J., ‘Groups with multiple operators’, Proc. London Math. Soc. 3 (1956), 366–416.CrossRefGoogle Scholar
[5]Kurosh, A. G., Lectures on general algebra (translated by Hirsch, K. A.), Chelsea Publishing Co., New York, 1963.Google Scholar
[6]le Roux, H. J., Bydrae tot die radikaalteorie in assosiati ewe ringe, Doctoral Thesis, University of the Orange Free State, Bloemfontein, 1978.Google Scholar
[7]Rjabuhin, Ju. M., ‘Radicals of Ω-groups I, general theory’, (in Russian) Mat. Issled. 3 (1968), 123–160.Google Scholar
[8]van der Walt, A. P. J., ‘Contributions to ideal theory in general rings’, Indag. Math. 26 (1964), 68–77.CrossRefGoogle Scholar
[9]van der Walt, A. P. J., ‘Prime ideals and nil radicals in near-rings’, Arch. Math. 15 (1964), 408–414.CrossRefGoogle Scholar