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

Journal of the Australian Mathematical Society

L. Van Wyk¹ 

关键词: 16 A 21;    16 A 42;   

DOI  :  10.1017/S1446788700030135

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown