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

Sophie Frisch, Sarah Nakato*

*Corresponding author for this work

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)3716-3723
Number of pages8
JournalCommunications in Algebra
Volume48
Issue number9
Early online date3 Apr 2020
DOIs
Publication statusPublished - 1 Sep 2020

Keywords

  • factorization
  • non-unique factorization
  • irreducible elements
  • absolutely irreducible elements
  • atoms
  • strong atoms
  • atomic domains
  • integer-valued polynomials
  • simple graphs
  • connected graphs
  • Factorization

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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