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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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]**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)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
13C05

Retrieve articles in all journals with MSC: 13C05

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