Journal of Commutative Algebra

Pseudo-convergent sequences and Prüfer domains of integer-valued polynomials

K. Alan Loper and Nicholas J. Werner

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Abstract

Let $K$ be a field with rank one valuation and $V$ the valuation domain of $K$. For a subset $E$ of $V$, the ring of integer-valued polynomials on $E$ is \[ \Int (E, V) = \{f \in K[x] \mid f(E) \subseteq V \}. \] A question of interest regarding $\Int (E, V)$ is: for which $E$ is $\Int (E, V)$ a Pr\"{u}fer domain? In this paper, we contribute a partial answer to this question. We classify exactly when $\Int (E, V)$ is Pr\"{u}fer in the case where the elements of $E$ comprise a pseudo-convergent sequence in $V$. Our work expands on earlier results that apply when $V$ is a discrete valuation domain.

Article information

Source
J. Commut. Algebra, Volume 8, Number 3 (2016), 411-429.

Dates
First available in Project Euclid: 9 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.jca/1473428566

Digital Object Identifier
doi:10.1216/JCA-2016-8-3-411

Mathematical Reviews number (MathSciNet)
MR3546004

Zentralblatt MATH identifier
1345.13013

Subjects
Primary: 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
Secondary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations

Keywords
Integer-valued polynomial pseudo-convergent Prüfer domain

Citation

Loper, K. Alan; Werner, Nicholas J. Pseudo-convergent sequences and Prüfer domains of integer-valued polynomials. J. Commut. Algebra 8 (2016), no. 3, 411--429. doi:10.1216/JCA-2016-8-3-411. https://projecteuclid.org/euclid.jca/1473428566


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