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An Almost Krull Domain with Divisorial Height One Primes

Published online by Cambridge University Press:  20 November 2018

J. T. Arnold  and
Ryuki Matsuda
J. T. Arnold
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia24061
Ryuki Matsuda
Affiliation:
Ibaraki University, Mito, Ibaraki 310, Japan
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Abstract

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E. Pirtle has conjectured that if D is an almost Krull domain in which the height one prime ideals are divisorial then D is a Krull domain. An example is given to show that this is not the case. Further, let U = and let denote the set of prime ideals of D which are minimal over some ideal (a):(b), where a, b ∈ D. If Dp is a valuation ring for each let then Huckaba and Papick have asked whether D[x]U must be a Prufer domain. The given example shows that it need not be.

Keywords

13G0513F99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 50 - 53
Copyright
Copyright © Canadian Mathematical Society 1986

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