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STRONGLY IRREDUCIBLE IDEALS

Published online by Cambridge University Press:  01 April 2008

A. AZIZI*
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran (email: aazizi@shirazu.ac.ir, a_azizi@yahoo.com)
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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.

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

References

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