On the infinitude of prime elements

Let R be an infinite unique factorization domain with at most finitely many units. We discuss the infinitude of prime elements in R when R is arbitrary and when R satisfies the following property: if f and g are polynomials with coefficients in R such that f(r) divides g(r) for all rε R with f(r)≠ 0...

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Autores:: Cáceres-Duque, Luis F.
Vélez-Marulanda, José A.

Tipo de recurso:: Article of journal

Fecha de publicación:: 2013

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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spelling	Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cáceres-Duque, Luis F.96f373a2-1eb6-4e0a-9050-4484547f53ae300Vélez-Marulanda, José A.674ca3ca-7843-49e4-8bcf-985ef661932b3002019-06-29T08:36:33Z2019-06-29T08:36:33Z2013https://repositorio.unal.edu.co/handle/unal/49341http://bdigital.unal.edu.co/42798/Let R be an infinite unique factorization domain with at most finitely many units. We discuss the infinitude of prime elements in R when R is arbitrary and when R satisfies the following property: if f and g are polynomials with coefficients in R such that f(r) divides g(r) for all rε R with f(r)≠ 0, then either g=0 or deg(f) ≤ deg(g).Sea R un dominio de factorización única que tiene a lo sumo un número finito de unidades. Nosotros discutimos la infinitud de elementos primos en R cuando R es arbitrario y cuando Rsatisface la siguiente propiedad: si f y g son polinomios con coeficientes en R tales que f(r)divide g(r) para todo rε R con f(r)≠ 0, entonces g=0 ó grado(f) ≤ grado(g).application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/45184Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 167-179 2357-4100 0034-7426Cáceres-Duque, Luis F. and Vélez-Marulanda, José A. (2013) On the infinitude of prime elements. Revista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 167-179 2357-4100 0034-7426 .On the infinitude of prime elementsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTDominios de factorización únicaelementos primos11A4113G99Unique factorization domainsPrime elements11A4113G99ORIGINAL45184-216921-2-PB.htmltext/html4845https://repositorio.unal.edu.co/bitstream/unal/49341/1/45184-216921-2-PB.html198709b880c97085366394ffa5ea5354MD5145184-216920-1-SM.pdfapplication/pdf456314https://repositorio.unal.edu.co/bitstream/unal/49341/2/45184-216920-1-SM.pdfeaca378e7bc5334685cef8f3bebd05bbMD52THUMBNAIL45184-216920-1-SM.pdf.jpg45184-216920-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5487https://repositorio.unal.edu.co/bitstream/unal/49341/3/45184-216920-1-SM.pdf.jpga4a14351de197e451fbf1d66e51ae0e8MD53unal/49341oai:repositorio.unal.edu.co:unal/493412022-12-14 23:03:59.967Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv	On the infinitude of prime elements
title	On the infinitude of prime elements
spellingShingle	On the infinitude of prime elements Dominios de factorización única elementos primos 11A41 13G99 Unique factorization domains Prime elements 11A41 13G99
title_short	On the infinitude of prime elements
title_full	On the infinitude of prime elements
title_fullStr	On the infinitude of prime elements
title_full_unstemmed	On the infinitude of prime elements
title_sort	On the infinitude of prime elements
dc.creator.fl_str_mv	Cáceres-Duque, Luis F. Vélez-Marulanda, José A.
dc.contributor.author.spa.fl_str_mv	Cáceres-Duque, Luis F. Vélez-Marulanda, José A.
dc.subject.proposal.spa.fl_str_mv	Dominios de factorización única elementos primos 11A41 13G99 Unique factorization domains Prime elements 11A41 13G99
topic	Dominios de factorización única elementos primos 11A41 13G99 Unique factorization domains Prime elements 11A41 13G99
description	Let R be an infinite unique factorization domain with at most finitely many units. We discuss the infinitude of prime elements in R when R is arbitrary and when R satisfies the following property: if f and g are polynomials with coefficients in R such that f(r) divides g(r) for all rε R with f(r)≠ 0, then either g=0 or deg(f) ≤ deg(g).
publishDate	2013
dc.date.issued.spa.fl_str_mv	2013
dc.date.accessioned.spa.fl_str_mv	2019-06-29T08:36:33Z
dc.date.available.spa.fl_str_mv	2019-06-29T08:36:33Z
dc.type.spa.fl_str_mv	Artículo de revista
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dc.relation.spa.fl_str_mv	http://revistas.unal.edu.co/index.php/recolma/article/view/45184
dc.relation.ispartof.spa.fl_str_mv	Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv	Revista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 167-179 2357-4100 0034-7426
dc.relation.references.spa.fl_str_mv	Cáceres-Duque, Luis F. and Vélez-Marulanda, José A. (2013) On the infinitude of prime elements. Revista Colombiana de Matemáticas; Vol. 47, núm. 2 (2013); 167-179 2357-4100 0034-7426 .
dc.rights.spa.fl_str_mv	Derechos reservados - Universidad Nacional de Colombia
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On the infinitude of prime elements

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