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arXiv · 2208.09935

Ring Structure of Integer-Valued Rational Functions

Baian Liu
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Abstract

$\DeclareMathOperator{\IntR}{Int{}^\text{R}}$Integer-valued rational functions are a natural generalization of integer-valued polynomials. Given a domain $D$, the collection of all integer-valued rational functions over $D$ forms a ring extension $\IntR(D)$ of $D$. For a valuation domain $V$, we characterize when $\IntR(V)$ is a Pr\"ufer domain and when $\IntR(V)$ is a B\'ezout domain. We also extend the classification of when $\IntR(D)$ is a Pr\"ufer domain.

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Baian Liu. 2022-08-21. Ring Structure of Integer-Valued Rational Functions. https://arxiv.org/abs/2208.09935

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