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A negative answer to the prime sequence question


Author: Raymond C. Heitmann
Journal: Proc. Amer. Math. Soc. 77 (1979), 23-26
MSC: Primary 13C05
DOI: https://doi.org/10.1090/S0002-9939-1979-0539623-7
MathSciNet review: 539623
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Abstract: If P is a complete intersection prime, i.e., a prime ideal generated by $ ht(P)$ elements, in a Noetherian domain, can P be generated by a prime sequence, a regular sequence whose initial segments generate prime ideals? The purpose of this article is to present an example showing that this question, the Prime Sequence Question, has a negative answer. The example is a two-dimensional integrally closed domain with a height two complete intersection prime which contains no prime elements.


References [Enhancements On Off] (What's this?)

  • [1] E. Davis, Prime ideals and prime sequences in polynomial rings, Proc. Amer. Math. Soc. 72 (1978), 33-38. MR 0498533 (58:16640)
  • [2] W. Heinzer and J. Ohm, Noetherian intersections of integral domains, Trans. Amer. Math. Soc. 167 (1972), 291-308. MR 0296095 (45:5156)
  • [3] R. Heitmann, Prime ideal posets in Noetherian rings, Rocky Mountain J. Math. 7 (1977), 667-673. MR 0444642 (56:2992)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0539623-7
Keywords: Noetherian ring, prime sequence, complete intersection prime, valuation
Article copyright: © Copyright 1979 American Mathematical Society

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