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STRONGLY IRREDUCIBLE IDEALS

Part of: General commutative ring theory Chain conditions, finiteness conditions Arithmetic rings and other special rings Theory of modules and ideals

Published online by Cambridge University Press:  01 April 2008

A. AZIZI
A. AZIZI*
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran (email: [email protected], [email protected])
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Abstract

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A proper ideal I of a ring R is said to be strongly irreducible if for each pair of ideals A and B of R, implies that either or . In this paper we study strongly irreducible ideals in different rings. The relations between strongly irreducible ideals of a ring and strongly irreducible ideals of localizations of the ring are also studied. Furthermore, a topology similar to the Zariski topology related to strongly irreducible ideals is introduced. This topology has the Zariski topology defined by prime ideals as one of its subspace topologies.

Keywords

absolutely flat ringsarithmetical ringsgeneralizations of Dedekind domainsLaskerian ringsstrongly irreducible idealsZariski topology

MSC classification

Secondary: 13A15: Ideals; multiplicative ideal theory 13C05: Structure, classification theorems 13E05: Noetherian rings and modules 13F99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 145 - 154
Copyright
Copyright © 2008 Australian Mathematical Society

References

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