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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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References
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[1]Atiyah M. F. and MacDonald I. G., Introduction to Commutative Algebra (Addison-Wesley, Reading, MA, 1969).
[2]Heinzer W. J., Ratliff L. J. Jr and Rush D. E., ‘Strongly irreducible ideals of a commutative ring’, J. Pure Appl. Algebra 166 (2002), 267275.
[3]Jensen C., ‘Arithmetical rings’, Acta Math. Sci. Acad. Sci. Hungar. 17 (1966), 115123.
[4]Larsen M. D. and McCarthy P. J., Multiplicative Theory of Ideals (Academic Press, New York, 1971).
[5]Matsumura H., Commutative Ring Theory (Cambridge University Press, Cambridge, 1992).
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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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