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The -radical in structural matrix near rings, II

Published online by Cambridge University Press:  14 November 2011

Leon van Wyk
Leon van Wyk
Affiliation:
Department of Mathematics, University of Stellenbosch, Stellenbosch 7600, South Africa
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Synopsis

Whether the -radical of a structural matrix near-ring (B, R) is the sum of two non-trivial ideals, one of which is nilpotent, is an open problem. However, it is known that ((B, R)) contains two ideals and , which are respectively precisely the two ideals, the sum of which is the Jacobson radical, in the case where the underlying near-ring is a ring. We strengthen our conjecture that and are the sought-after ideals by showing that (B, R)/≅(C, R) in the near-ring case, where C is the largest symmetric Boolean matrix such that C≦B, and by showing that is nilpotent.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 1-2 , 1992 , pp. 53 - 61
Copyright
Copyright © Royal Society of Edinburgh 1992

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