Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T00:37:56.014Z Has data issue: false hasContentIssue false
  • English
  • Français

On primeness and nilpotence in structural matrix near-rings

Published online by Cambridge University Press:  20 January 2009

Enoch K. S. Lee
Enoch K. S. Lee
Affiliation:
Mathematics Department University of Southwestern Louisiana Lafayette, LA 70504, U.S.A.
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 structure of completely prime ideals in any structural matrix near-rings is determined. Partial descriptions are obtained for prime, nil, nilpotent, and locally nilpotent ideals of structural matrix near-rings. Their associated radicals are also studied in this paper.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 345 - 356
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Bhandari, M. C. and Sexana, P. K., A note on Levitski radical of near-ring, Kyungpook Math. J. 20 (1980), 183–188.Google Scholar
2. Birkenmeier, G., Heatherly, H. and Lee, E., Prime ideals and prime radicals in near-rings, Monatsh. Math. 117 (1994), 179–197.CrossRefGoogle Scholar
3. Birkenmeier, G., Heatherly, H. and Lee, E., Completely prime ideals and associated radicals, in Ring Theory (Proceedings of the Ohio State-Denison Conference, 1992, Jain, S. K. and Rizvi, S. T., eds., World Scientific, Singapore, 1993).Google Scholar
4. Booth, G. L. and Groenewald, N. J., On primeness in matrix near-rings, Arch. Math. 56 (1991), 539–546.CrossRefGoogle Scholar
5. Groenewald, N. J., Different prime ideals in near-rings, Comm. Algebra 19 (1991), 2667–2675.CrossRefGoogle Scholar
6. Groenewald, N. J. and Potgieter, P. C., A note on the Levitzki radical of a near-ring, J. Austral. Math. Soc. Ser. A 36 (1984), 416–420.CrossRefGoogle Scholar
7. Lee, E., Prime ideals in structural matrix near-rings, Tamkang J. Math. 26 (1995), 31–40.CrossRefGoogle Scholar
8. Meldrum, J. D. P., Matrix near-rings, in Contributions to General Algebra 8 (Proceedings of the Conference on Near-Rings and Near-Fields, 07 14–20, 1991, Pilz, G., ed.), Verlag Hölder-Pichler-Tempsky), 189–204.Google Scholar
9. Meldrum, J. D. P. and Van Der Walt, A. P. J., Matrix near-rings, Arch. Math. 47 (1986), 312–319.CrossRefGoogle Scholar
10. Van Der Walt, A. P. J., On two-sided ideals in matrix near-rings, in Near-Rings and Near Fields (G. Betsch, ed., 1987), 267–271.CrossRefGoogle Scholar
11. Van Der Walt, A. P. J. and Van Wyk, L., The J2-radical in structural matrix near-rings, J. Algebra 123 (1989), 248–261.CrossRefGoogle Scholar