A negative answer to the prime sequence question
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- by Raymond C. Heitmann PDF
- Proc. Amer. Math. Soc. 77 (1979), 23-26 Request permission
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
- Edward D. Davis, Prime elements and prime sequences in polynomial rings, Proc. Amer. Math. Soc. 72 (1978), no. 1, 33–38. MR 498533, DOI 10.1090/S0002-9939-1978-0498533-3
- William Heinzer and Jack Ohm, Noetherian intersections of integral domains, Trans. Amer. Math. Soc. 167 (1972), 291–308. MR 296095, DOI 10.1090/S0002-9947-1972-0296095-6
- Raymond C. Heitmann, Prime ideal posets in Noetherian rings, Rocky Mountain J. Math. 7 (1977), no. 4, 667–673. MR 444642, DOI 10.1216/RMJ-1977-7-4-667
Additional Information
- © Copyright 1979 American Mathematical Society
- 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