A Negative Answer to the Prime Sequence Question

Abstract

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.