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On semiprime segments of rings

Published online by Cambridge University Press:  09 April 2009

R. Mazurek
Affiliation:
Faculty of Computer Science, Bialystok Technical University, Wiejska 45A, 15–351 Bialystok, Poland, e-mail: [email protected]
G. Törner
Affiliation:
Institut für Mathematik, Fakultät 4, Universität Duisburg-Essen, Campus Duisburg47048 Duisburg, Germany, e-mail: [email protected]
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Abstract

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A semiprime segment of a ring R is a pair P2P1 of semiprime ideals of R such that ∩ InP2 for all ideals I of R with P2IP1. In this paper semiprime segments with P1 a comparizer ideal are classified as either simple, exceptional, or archimedean, extending to several classes of rings a classification known for right chain rings. These three types of semiprime segments are also characterized in terms of the pseudo-radical.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

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