A negative answer to the prime sequence question

Author:
Raymond C. Heitmann

Journal:
Proc. Amer. Math. Soc. **77** (1979), 23-26

MSC:
Primary 13C05

MathSciNet review:
539623

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Abstract: If *P* is a complete intersection prime, i.e., a prime ideal generated by 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.

**[1]**Edward D. Davis,*Prime elements and prime sequences in polynomial rings*, Proc. Amer. Math. Soc.**72**(1978), no. 1, 33–38. MR**0498533**, 10.1090/S0002-9939-1978-0498533-3**[2]**William Heinzer and Jack Ohm,*Noetherian intersections of integral domains*, Trans. Amer. Math. Soc.**167**(1972), 291–308. MR**0296095**, 10.1090/S0002-9947-1972-0296095-6**[3]**Raymond C. Heitmann,*Prime ideal posets in Noetherian rings*, Rocky Mountain J. Math.**7**(1977), no. 4, 667–673. MR**0444642**

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DOI:
http://dx.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