Abstract
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.
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