论文标题
整数值有理函数的环结构
Ring Structure of Integer-Valued Rational Functions
论文作者
论文摘要
$ \ DECTAREMATHOPERATOR {\ inter} {int {}^\ text {r}} $ integer-valued Rication函数是整数值多项式的自然概括。给定域$ d $，收集了$ d $以上的所有整数价值有理功能，形成了$ d $的$ \ intress $ \ inter（d）$。对于评估域$ v $，我们表征$ \ int（v）$是一个prüfer域，而$ \ intr（v）$是bézout域。我们还将$ \ int（d）$的分类扩展为Prüfer域。
$\DeclareMathOperator{\IntR}{Int{}^\text{R}}$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 Prüfer domain and when $\IntR(V)$ is a Bézout domain. We also extend the classification of when $\IntR(D)$ is a Prüfer domain.
