Open Access
2016 Pseudo-convergent sequences and Prüfer domains of integer-valued polynomials
K. Alan Loper, Nicholas J. Werner
J. Commut. Algebra 8(3): 411-429 (2016). DOI: 10.1216/JCA-2016-8-3-411


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.


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K. Alan Loper. Nicholas J. Werner. "Pseudo-convergent sequences and Prüfer domains of integer-valued polynomials." J. Commut. Algebra 8 (3) 411 - 429, 2016.


Published: 2016
First available in Project Euclid: 9 September 2016

zbMATH: 1345.13013
MathSciNet: MR3546004
Digital Object Identifier: 10.1216/JCA-2016-8-3-411

Primary: 13F20
Secondary: 13F05

Keywords: integer-valued polynomial , Prüfer domain , pseudo-convergent

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.8 • No. 3 • 2016
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