论文标题
整数价值多项式I的不可约性I
Irreducibility of integer-valued polynomials I
论文作者
论文摘要
令$ s \子集r $为独特分解域$ r $的任意子集，而$ \ k $是$ r $的分数的字段。 The ring of integer-valued polynomials over $S$ is the set $\mathrm{Int}(S,R)= \{ f \in \mathbb{K}[x]: f(a) \in R\ \forall\ a \in S \}.$ This article is an effort to study the irreducibility of integer-valued polynomials over arbitrary subsets独特的分解域。我们提供了一种构建特殊序列的方法，我们称之为$ d $序列。然后，我们使用这些序列来获得一个标准，以确定多项式在$ \ mathrm {int}（s，s，r）中。$在某些特殊情况下，我们明确构建了这些序列，并使用这些序列来检查某些多项式在$ \ mathrm {int}（int}（s，s，s，s，s，s，s，s，s in）中的不可否认性。 Dedekind域。
Let $S \subset R$ be an arbitrary subset of a unique factorization domain $R$ and $\K$ be the field of fractions of $R$. The ring of integer-valued polynomials over $S$ is the set $\mathrm{Int}(S,R)= \{ f \in \mathbb{K}[x]: f(a) \in R\ \forall\ a \in S \}.$ This article is an effort to study the irreducibility of integer-valued polynomials over arbitrary subsets of a unique factorization domain. We give a method to construct special kinds of sequences, which we call $d$-sequences. We then use these sequences to obtain a criteria for the irreducibility of the polynomials in $\mathrm{Int}(S,R).$ In some special cases, we explicitly construct these sequences and use these sequences to check the irreducibility of some polynomials in $\mathrm{Int}(S,R).$ At the end, we suggest a generalization of our results to an arbitrary subset of a Dedekind domain.
