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  • 1 Sichuan Normal University, Chengdu, Sichuan, 610068, P.R. China
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In this paper, we concern the Principal Ideal Theorem (PIT) for w-Noetherian rings. Let R be a w-Noetherian ring and a be a nonzero nonunit element of R. If p is a prime ideal of R minimal over (a), then ht p ≦ 1.

  • [1]

    Barucci, V., Anderson, D. F. and Dobbs, D. E., Coherent Mori domains and the Principal Ideal Theorem, Comm. Algebra, 15 (1987), 11191156.

    • Search Google Scholar
    • Export Citation
  • [2]

    Chen, Y. H. and Yin, H. Y., The Principal Ideal Theorem for modules, J. Sichuan Norm. Univ., 32 (2009), 269272 (in Chinese).

  • [3]

    Chang, G. W., On the Principal Ideal Theorem, Bull. Korean Math. Soc., 36 (1999), 655660.

  • [4]

    Huckaba, J. A., Commutative Rings with Zero Divisors, Marcel Dekker, New York, 1988.

  • [5]

    Kaplansky, I., Commutative Rings (Revised ed.), Univ. of Chicago Press, Chicago, 1974.

  • [6]

    Wang, F. G. and McCasland, R. L., On strong Mori domains, J. Pure Appl. Algebra, 135 (1999), 155165.

  • [7]

    Wang, F. G. and Zhang, J., Injective modules over w-Noetherian rings, Acta Mathematica Sinica (Chinese Series), 53 (2010), 11191130.

    • Search Google Scholar
    • Export Citation
  • [8]

    Yin, H. Y., Wang, F. G., Zhu, X. S. and Chen, Y. H., w-Modules over commutative rings, J. Korean Math. Soc., 48 (2011), 207222.

  • [9]

    Yin, H. Y. and Chen, Y. H., w-overrings of w-Noetherian rings, Studia Sci. Math. Hungar., 49 (2012), 200205.