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Prime and special ideals in structural matrix rings over a ring without unity

Published online by Cambridge University Press:  09 April 2009

L. Van Wyk
L. Van Wyk
Affiliation:
Department of Mathematics, University of Stellenbosch7600 Stellenbosch, South Africa
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Abstract

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A. D. Sands showed that there is a 1–1 correspondence between the prime ideals of an arbitraty associative ring R and the complete matrix ring Mn(R) via P→ Mn(P). A structural matrix ring M(B, R) is the ring of all n × n matrices over R with 0 in the positions where the n × n boolean matrix B, B a quasi-order, has 0. The author characterized the special ideals of M(B, R′), in case R′ has unity, for certain special lasses of rings. In this note results of sands and the author are generalized to structural matrix rings over rings without unity. I t turns out that, although the class of prime simple rings is not a special class, Nagata's M-radical has the same form in structural matrix rings as the special radicals studied by the author.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 220 - 226
Copyright
Copyright © Australian Mathematical Society 1988

References

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