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STRONGLY IRREDUCIBLE IDEALS

  • A. AZIZI (a1)
Abstract
Abstract

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.

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[2]W. J. Heinzer , L. J. Ratliff Jr and D. E. Rush , ‘Strongly irreducible ideals of a commutative ring’, J. Pure Appl. Algebra 166 (2002), 267275.

[3]C. Jensen , ‘Arithmetical rings’, Acta Math. Sci. Acad. Sci. Hungar. 17 (1966), 115123.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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