On the distribution of prime elements in polynomial Krull domains
Authors:
D. Costa, L. Gallardo and J. Querré
Journal:
Proc. Amer. Math. Soc. 87 (1983), 41-43
MSC:
Primary 13F15; Secondary 13A17, 13F05
DOI:
https://doi.org/10.1090/S0002-9939-1983-0677227-7
MathSciNet review:
677227
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Abstract: Let be a Krull domain having infinitely many height one primes. It is shown that any ideal of height two in the polynomial ring
contains a prime element. An application to the construction of Dedekind domains with specified class groups is given, along with an example to show the necessity of assuming infinitely many height one primes.
- [1] Robert M. Fossum, The divisor class group of a Krull domain, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 74. MR 0382254
- [2] Julien Querré, Idéaux divisoriels d’un anneau de polynômes, J. Algebra 64 (1980), no. 1, 270–284 (French). MR 575795, https://doi.org/10.1016/0021-8693(80)90146-5
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DOI:
https://doi.org/10.1090/S0002-9939-1983-0677227-7
Article copyright:
© Copyright 1983
American Mathematical Society