J Austral Math Soc Ser A 46 pp262--271, 1989.

On the Small and Essential Ideals in Certain Classes of Rings

B. W. Green and L. van Wyk

(Received 11 September 1987)

Abstract

It is well known that for a ring with identity the Brown-McCoy radical is the maximal small ideal. However, in certain subrings of complete matrix rings, which we call structural matrix rings, the maximal small and minimal essential ideals coincide. In this paper we characterize a class of commutative and a class of non-commutative rings for which this coincidence occurs, namely quotients of Prüfer domains and structural matrix rings over Brown-McCoy semisimple rings. A similarity between these two classes is obtained.

1980 AMS Subject Classification (1985 Revision): 13F05, 16A42, 16A66

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Authors

B. W. Green
L. van Wyk: Department of Mathematics, University of Stellenbosch, Stellenbosch 7600, Republic of South Africa.

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