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On semiprime segments of rings

Part of: Modules, bimodules and ideals Rings and algebras with additional structure

Published online by Cambridge University Press:  09 April 2009

R. Mazurek  and
G. Törner
R. Mazurek
Affiliation:
Faculty of Computer Science, Bialystok Technical University, Wiejska 45A, 15–351 Bialystok, Poland, e-mail: mazurek@pb.bialystok.pl
G. Törner
Affiliation:
Institut für Mathematik, Fakultät 4, Universität Duisburg-Essen, Campus Duisburg47048 Duisburg, Germany, e-mail: toerner@math.uni-duisburg.de
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Abstract

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A semiprime segment of a ring R is a pair P2 ⊂ P1 of semiprime ideals of R such that ∩ In ⊆ P2 for all ideals I of R with P2 ⊂ I ⊂ P1. 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.

MSC classification

Secondary: 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation 16W99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 2 , April 2006 , pp. 263 - 272
Copyright
Copyright © Australian Mathematical Society 2006

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