A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator

Sophie Frisch, Sarah Nakato*

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of the ring (Formula presented.) of integer-valued polynomials on a principal ideal domain D with quotient field K, we give an easy to verify graph-theoretic sufficient condition for an element to be absolutely irreducible and show a partial converse: the condition is necessary and sufficient for polynomials with square-free denominator.

Originalspracheenglisch
Seiten (von - bis)3716-3723
Seitenumfang8
FachzeitschriftCommunications in Algebra
Jahrgang48
Ausgabenummer9
Frühes Online-Datum3 Apr 2020
DOIs
PublikationsstatusVeröffentlicht - 1 Sep 2020

ASJC Scopus subject areas

  • !!Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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