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

 

Integer-valued polynomials over Krull-type domains and Prüfer $v$-multiplication domains


Author: Francesca Tartarone
Journal: Proc. Amer. Math. Soc. 128 (2000), 1617-1625
MSC (1991): Primary 13A15, 13A18, 13B25; Secondary 13B30
Published electronically: October 18, 1999
MathSciNet review: 1641121
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Abstract: Let $D$ be a domain with quotient field $K$. The ring of integer-valued polynomials over $D$ is $\text{Int}(D) := \{f \in K[X]; f(D) \subseteq D\}$. We characterize the Krull-type domains $D$ such that $\text{Int}(D)$ is a Prüfer $v$-multiplication domain.


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Additional Information

Francesca Tartarone
Affiliation: Faculté des Sciences de Saint-Jérôme, Université d’Aix-Marseille III, 13397 Marseille, France
Address at time of publication: Dipartimento di Matematica, Università degli Studi di Roma “Roma Tre”, Largo Murialdo 1 00146 Roma, Italy
Email: francesca.tartarone@vmesa12.u-3mrs.fr, tfrance@matrm3.mat.uniroma3.it

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05174-6
PII: S 0002-9939(99)05174-6
Received by editor(s): March 5, 1998
Received by editor(s) in revised form: July 22, 1998
Published electronically: October 18, 1999
Additional Notes: The author would like to thank Prof. Stefania Gabelli who introduced her to this topic and who gave her useful advice for this work. She also would like to thank the Laboratoire des Mathématiques de la Faculté des Sciences de Saint-Jérôme in Marseille where she is attending a Post-Doc research program and Prof. P.-J. Cahen who carefully read this paper providing valuable suggestions
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society