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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Schwartz, Niels 2016. Strongly Irreducible Ideals and Truncated Valuations. Communications in Algebra, Vol. 44, Issue. 3, p. 1055.


    ABUHLAIL, JAWAD and LOMP, CHRISTIAN 2013. ON THE NOTION OF STRONG IRREDUCIBILITY AND ITS DUAL. Journal of Algebra and Its Applications, Vol. 12, Issue. 06, p. 1350012.


    Nikseresht, A. and Azizi, A. 2013. Zariski spaces of modules. Journal of Pure and Applied Algebra, Vol. 217, Issue. 7, p. 1187.


    Juett, Jason 2012. Generalized comaximal factorization of ideals. Journal of Algebra, Vol. 352, Issue. 1, p. 141.


    Nikmehr, M. J. and Fatahi, F. 2011. Remarks on α-strongly irreducible ideals. Frontiers of Mathematics in China, Vol. 6, Issue. 5, p. 901.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 84, Issue 2
  • April 2008, pp. 145-154

STRONGLY IRREDUCIBLE IDEALS

  • A. AZIZI (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788708000062
  • Published online: 01 April 2008
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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