Irreducibility of integer-valued polynomials I

• Published in: Communications in algebra Vol. 49; no. 3; pp. 948 - 955
• Main Author: Prasad, Devendra
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04-03-2021; Taylor & Francis Ltd
• Subjects: Domains; Factorization; Integer-valued polynomials; Integers; irreducible elements; Polynomials; Rings (mathematics)
• ISSN: 0092-7872; 1532-4125
• DOI: 10.1080/00927872.2020.1823990

Let
be an arbitrary subset of a unique factorization domain R and
be the field of fractions of R. The ring of integer-valued polynomials over S is the set
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
In some special cases, we explicitly construct these sequences and use these sequences to check the irreducibility of some polynomials in
At the end, we suggest a generalization of our results to an arbitrary subset of a Dedekind domain.