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

The ring of integer-valued polynomials of a Dedekind domain


Authors: Robert Gilmer, William Heinzer, David Lantz and William Smith
Journal: Proc. Amer. Math. Soc. 108 (1990), 673-681
MSC: Primary 13F20; Secondary 11R09, 13B25, 13F05
MathSciNet review: 1009989
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Abstract: Let $ D$ be a Dedekind domain and $ R = Int(D)$ be the ring of integer-valued polynomials of $ D$. We relate the ideal class groups of $ D$ and $ R$. In particular we prove that, if $ D = \mathbb{Z}$ is the ring of rational integers, then the ideal class group of $ R$ is a free abelian group on a countably infinite basis.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1009989-7
PII: S 0002-9939(1990)1009989-7
Keywords: ring of integer-valued polynomials, invertible ideals, Picard group
Article copyright: © Copyright 1990 American Mathematical Society