Irreducible polynomials in Int⁡(Z).

Sarah Nakato, Roswitha Rissner, Austin Antoniou

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

In order to fully understand the factorization behavior of the ring Int(ℤ) = {f ∈ ℚ[x] | f (ℤ) ⊆ ℤ} of integer-valued polynomials on ℤ, it is crucial to identify the irreducible elements. Peruginelli [8] gives an algorithmic criterion to recognize whether an integer-valued polynomial g/d is irreducible in the case where d is a square-free integer and g ∈ ℤ[x] has fixed divisor d. For integer-valued polynomials with arbitrary composite denominators, so far there is no algorithmic criterion known to recognize whether they are irreducible. We describe a computational method which allows us to recognize all irreducible polynomials in Int(ℤ). We present some known facts, preliminary new results and open questions.
Original languageEnglish
Title of host publicationITM Web of Conferences
Number of pages10
Volume20
DOIs
Publication statusPublished - 12 Oct 2018

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    Nakato, S., Rissner, R., & Antoniou, A. (2018). Irreducible polynomials in Int⁡(Z). In ITM Web of Conferences (Vol. 20). [01004] https://doi.org/10.1051/itmconf/20182001004