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

DOI10.1080/00927872.2020.1744618zbMath1451.13065arXiv1912.10535OpenAlexW3015100553WikidataQ99557786 ScholiaQ99557786MaRDI QIDQ5131740

Sarah Nakato, Sophie Frisch

Publication date: 9 November 2020

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.10535

zbMATH Keywords

connected graphinteger-valued polynomialsabsolutely irreducible element

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Polynomials over commutative rings (13B25) Polynomials, factorization in commutative rings (13P05) Divisibility and factorizations in commutative rings (13A05)

Related Items

Split absolutely irreducible integer-valued polynomials over discrete valuation domains, Absolute irreducibility of the binomial polynomials, Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations, Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains, Strong atoms in monadically Krull monoids, Divisibility in rings of integer-valued polynomials

Cites Work

• Elasticity for integral-valued polynomials
• Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields
• A NEW CHARACTERIZATION OF HALF-FACTORIAL KRULL MONOIDS
• An arithmetic characterization of algebraic number fields with a given class group
• A pure arithmetical characterization for certain fields with a given class group
• Non-absolutely irreducible elements in the ring of integer-valued polynomials
• Factorization of Integer-Valued Polynomials with Square-Free Denominator
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