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On the small and essential ideals in certain classes of rings

Part of: Arithmetic rings and other special rings

Published online by Cambridge University Press:  09 April 2009

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

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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.

MSC classification

Secondary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 262 - 271
Copyright
Copyright © Australian Mathematical Society 1989

References

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[5]Van Wyk, L., ‘Special radicals in structural matrix rings’, Comm. Algebra 16 (1988), 421–435.Google Scholar