Bhargava factorials and irreducibility of integer-valued polynomials

2021/09/27 by Prasad, Devendra
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.12867

Abstract

The ring of integer-valued polynomials over a given subset S of \Z (or Int(S,\Z )) is defined as the set of polynomials in \Q[x] which maps S to \Z. In factorization theory, it is crucial to check the irreducibility of a polynomial. In this article, we make Bhargava factorials our main tool to check the irreducibility of a given polynomial f ∈ Int(S,\Z )). We also generalize our results to arbitrary subsets of a Dedekind domain.

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