Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-09T15:36:37.756Z Has data issue: false hasContentIssue false
  • English
  • Français

An antiradical for near-rings

Published online by Cambridge University Press:  14 November 2011

J. F. T. Hartney
J. F. T. Hartney
Affiliation:
Mathematics Department, University of the Witwatersrand, Johannesburg, South Africa
Get access Rights & Permissions [Opens in a new window]

Synopsis

Throughout this article, the near-ring N is assumed to be zero symmetric and to satisfy the right distributive law. We construct an ideal called the socle-ideal of N which is antiradical in the sense that it is a direct sum of minimal left ideals and annihilates one or more of the radicals of N. We then use this socle-ideal to obtain a decomposition theorem for the s-radical JS(N) of N.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 185 - 191
Copyright
Copyright © Royal Society of Edinburgh 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Baer, Reinhold. Radical ideals. Amer. J. Math. 65 (1943), 537–568.Google Scholar
2Betsch, Gerhard. Struktursatze fur Fastringe (Inaugural Dissertation, Eberhard-Karls-Universität, Tubingen).Google Scholar
3Blackett, D. W.. Simple and semi-simple near-rings. Proc. Amer. Math. Soc. 4 (1953), 772–785.Google Scholar
4Cohn, P. M. and Sasiada, E.. An example of a simple radical ring. J. Algebra 5 (1967), 373–377.Google Scholar
5Divinsky, N. J.. Rings and radicals (Toronto: Univ. of Toronto Press, 1965).Google Scholar
6Hartney, J. F. T.. Ph.D. thesis, University of Nottingham (1979).Google Scholar
7Hartney, J. F. T.. A radical for near-rings. Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 105–110.Google Scholar
8Laxton, R. R.. Prime ideals and the ideal radical of a distributively generated near-ring. Math. Z. 83 (1964), 8–17.CrossRefGoogle Scholar
9Laxton, R. R. and Machin, A. W.. On the decomposition of near-rings. Abh. Math. Sem. Univ. Hamburg 38 (1972), 221–230.Google Scholar
10Machin, A. W.. On a class of near-rings. Ph.D thesis, University of Nottingham (1971).Google Scholar
11Pilz, Giinter. Near-rings (Amsterdam: North Holland Math. Studies 23) (Amsterdam: North Holland, 1977).Google Scholar
12Scott, S. D.. Near-rings and near-rings modules. Ph.D thesis, Australian National University (1970).Google Scholar
13Scott, S. D.. Formation radicals for near-rings. Proc. London Math. Soc. 25 (1972), 441–464.Google Scholar