Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T02:37:17.358Z Has data issue: false hasContentIssue false

Two-sided ideals in group near-rings

Published online by Cambridge University Press:  09 April 2009

J. H. Meyer
Affiliation:
Department of Mathematics and Applied Mathematics, University of the Free State, PO Box 339, Bloemfontein 9300, South Africa e-mail: meyerjh.sci@mail.uovs.ac.za
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The two-sided ideals of group near-rings are characterized and studied. Various examples are presented to illustrate the interplay between ideals in the base near-ring R and the corresponding group near-ring R[G]. Some results concerning the Jacobson radicals of R[G] are also discussed.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Fray, R. L., ‘On ideals in group near-rings’, Acta Math. Hungar. 74 (1997), 155165.CrossRefGoogle Scholar
[2]le Riche, L. R., Meldrum, J. D. P. and van der Walt, A. P. J., ‘On group near-rings’, Arch. Math. 52 (1989), 132139.CrossRefGoogle Scholar
[3]Meldrum, J. D. P. and Meyer, J. H., ‘Intermediate ideals in matrix near-rings’, Comm. Algebra 24 (1996), 16011619.CrossRefGoogle Scholar
[4]Meldrum, J. D. P. and Meyer, J. H., ‘The J 0-radical of a matrix near-ring can be intermediate’, Canad. Math. Bull. 40 (1997), 198203.CrossRefGoogle Scholar
[5]Meldrum, J. D. P. and Meyer, J. H., ‘Word ideals in group near-rings’, Algebra Colloq. 5 (1998), 409416.Google Scholar
[6]Meldrum, J. D. P. and van der Walt, A. P. J., ‘Matrix near-rings’, Arch. Math. 47 (1986), 312319.CrossRefGoogle Scholar
[7]Meyer, J. H., Matrix near-rings (Ph.D. Thesis, University of Stellenbosch, 1986).Google Scholar
[8]Meyer, J. H., ‘Chains of intermediate ideals in matrix near-rings’, Arch. Math. 63 (1994), 311315.CrossRefGoogle Scholar
[9]Pilz, G., Near-rings, revised edition (North-Holland, Amsterdam, 1983).Google Scholar
[10]van der Walt, A. P. J., ‘Primitivity in matrix near-rings’, Quaestiones Math. 9 (1986), 459469.CrossRefGoogle Scholar
[11]van der Walt, A. P. J., ‘On two-sided ideals in matrix near-rings’, in: Near-rings and near-fields (Tübingen, 1985) (ed. Betsch, G.), North-Holland Math. Stud. 137 (North-Holland, Amsterdam, 1987) pp. 267272.Google Scholar