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

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 [Image: see text] of integer-valued polynomials on a principal ideal domain D with quotient field K, we give an...

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Detalles Bibliográficos
Autores principales: Frisch, Sophie, Nakato, Sarah
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Taylor & Francis 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7454568/
https://www.ncbi.nlm.nih.gov/pubmed/32939189
http://dx.doi.org/10.1080/00927872.2020.1744618
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author Frisch, Sophie
Nakato, Sarah
author_facet Frisch, Sophie
Nakato, Sarah
author_sort Frisch, Sophie
collection PubMed
description 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 [Image: see text] 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.
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spelling pubmed-74545682020-09-14 A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator Frisch, Sophie Nakato, Sarah Commun Algebra Article 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 [Image: see text] 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. Taylor & Francis 2020-04-03 /pmc/articles/PMC7454568/ /pubmed/32939189 http://dx.doi.org/10.1080/00927872.2020.1744618 Text en © 2020 The Author(s). Published with license by Taylor and Francis Group, LLC. https://creativecommons.org/licenses/by/4.0/This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Article
Frisch, Sophie
Nakato, Sarah
A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
title A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
title_full A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
title_fullStr A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
title_full_unstemmed A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
title_short A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
title_sort graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7454568/
https://www.ncbi.nlm.nih.gov/pubmed/32939189
http://dx.doi.org/10.1080/00927872.2020.1744618
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