Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

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

Author(s): Francesca Tartarone
Journal: Proc. Amer. Math. Soc. 128 (2000), 1617-1625.
MSC (1991): Primary 13A15, 13A18, 13B25; Secondary 13B30
Posted: October 18, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

[CC]
P.J. Cahen - J.-L. Chabert, Integer-Valued Polynomials, Math. Surveys and Monographs (AMS) 48 (1997). MR 98a:13002

[CH]
P.-J. Cahen - Y. Haouat, Polynômes à valeurs entières sur un anneau de pseudo-valuation, Manuscripta Math. 61 (1988), 23-31. MR 89f:13007

[Ch]
J.-L. Chabert, Anneaux de polynômes à valeurs entières et anneaux de Fatou, Bull. Sc. Math. France 99 (1971), 273-283. MR 46:1780

[Gi1]
R. Gilmer, Multiplicative Ideal Theory, Marcel-Dekker, New York (1972). MR 55:323

[Gi2]
R. Gilmer, Prüfer domains and rings of integer-valued polynomials, J. Algebra 129, n.2 (1990), 502-517. MR 91b:13023

[Gr]
M. Griffin, Some Results on $v$-multiplication Rings, Canad. J. Math. 10 (1967), 710-722. MR 35:6665

[HZ]
E.G. Houston - M. Zafrullah, Integral Domains in which each $t$-ideal is divisorial, Michigan Math. J. 35 (1988), 291-300. MR 89i:13027

[J]
P. Jaffard, Les Systèmes d'Idéaux, Dunod, Paris (1960). MR 22:5628

[K1]
B.G. Kang, Prüfer $v$-Multiplication Domains and the Ring $R[X]_{N_{v}}$, J. of Algebra 123 (1989), 151-170. MR 90e:13017

[K2]
B.G. Kang, Some questions about Prüfer $v$-Multiplication Domains, Comm. Algebra 17(3) (1989), 553-564. MR 90a:13033

[L]
A. Loper, A classification of all $D$ such that $\text{Int}(D)$ is a Prüfer domain, Proc. Amer. Math. Soc. (to appear).

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13A15, 13A18, 13B25, 13B30

Retrieve articles in all Journals with MSC (1991): 13A15, 13A18, 13B25, 13B30

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: 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
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google