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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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 $ 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0539623-7
PII: S 0002-9939(1979)0539623-7
Keywords: Noetherian ring, prime sequence, complete intersection prime, valuation
Article copyright: © Copyright 1979 American Mathematical Society