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Research Article

Irreducibility of integer-valued polynomials I

Pages 948-955 | Received 18 May 2020, Accepted 05 Sep 2020, Published online: 12 Dec 2020
 

Abstract

Let SR 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 Int(S,R)={fK[x]:f(a)RaS}. 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 Int(S,R). In some special cases, we explicitly construct these sequences and use these sequences to check the irreducibility of some polynomials in Int(S,R). At the end, we suggest a generalization of our results to an arbitrary subset of a Dedekind domain.

2010 Mathematics Subject Classification:

Acknowledgements

We thank Dr. A. Satyanarayana Reddy and Dr. Krishnan Rajkumar for their helpful suggestions. We also thank the referee for a careful reading of the manuscript and giving several suggestions to correct misprints and improve readability.

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