On the distribution of prime elements in polynomial Krull domains
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- by D. Costa, L. Gallardo and J. Querré PDF
- Proc. Amer. Math. Soc. 87 (1983), 41-43 Request permission
Abstract:
Let $A$ be a Krull domain having infinitely many height one primes. It is shown that any ideal of height two in the polynomial ring $A[t]$ 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.References
- Robert M. Fossum, The divisor class group of a Krull domain, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 74, Springer-Verlag, New York-Heidelberg, 1973. MR 0382254
- Julien Querré, Idéaux divisoriels d’un anneau de polynômes, J. Algebra 64 (1980), no. 1, 270–284 (French). MR 575795, DOI 10.1016/0021-8693(80)90146-5
Additional Information
- © Copyright 1983 American Mathematical Society
- 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