J Austral Math Soc Ser A 45 pp220--226, 1988.

Prime and Special Ideals in Structural Matrix Rings Over a Ring Without Unity

L. van Wyk

(Received 12 September 1986; revised 17 February 1987)

Abstract

A. D. Sands showed that there is a 1-1 correspondence between the prime ideals of an arbitrary associative ring R and the complete matrix ring M_n(R) via P Ž M_n(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 classes of rings. In this note results of Sands and the author are generalized to structural matrix rings over rings without unity. It 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.

1980 AMS Subject Classification: 16A21, 16A42

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Authors

L. van Wyk: Department of Mathematics, University of Stellenbosch, 7600 Stellenbosch, South Africa.

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Last Modified: Wed Feb 19 10:27:49 2003