Irreducibility of integer-valued polynomials I

Prasad, Devendra

doi:10.1080/00927872.2020.1823990

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2022

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Cited by 2 publications

(2 citation statements)

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“…In Prasad [5] , the concept of d-sequences was introduced for the first time to check the irreducibility of a given integer-valued polynomial. In this section, we generalize the definition of d-sequences to the case of several variables.…”

Section: M -Sequencesmentioning

confidence: 99%

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Irreducibility of integer-valued polynomials in several variables

Prasad¹

2021

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Let S be an arbitrary subset of R n 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 S, denoted by Int(S, R), is defined as the set of the polynomials of K[x], which maps S to R. In this article, we study the irreducibility of the polynomials of Int(S, 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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Section: M -Sequencesmentioning

confidence: 99%

“…Hence, we must be familiar with the irreducibility of a given polynomial. Recently, Prasad [5] gave a new approach to test the irreducibility of a given integer-valued polynomial in one variable. The cornerstone of this study was the construction of π-sequences and d-sequences, which we recall here for the sake of completeness.…”

Section: Introductionmentioning

confidence: 99%