Irreducibility of integer-valued polynomials in several variables

2021/08/17 by Prasad, Devendra
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.07458

Abstract

Let § be an arbitrary subset of Rⁿ where R is a domain with the field of fractions \K. Denote the ring of polynomials in n variables over \K by \K[\x]. The ring of integer-valued polynomials over §, denoted by Int(§,R), is defined as the set of the polynomials of \K[\x], which maps § to R. In this article, we study the irreducibility of the polynomials of Int(§,R) for the first time in the case when R is a Unique Factorization Domain. We also show that our results remain valid when R is a Dedekind domain or sometimes any domain.

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