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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.47 no.2 Bogotá July/Dec. 2013

 

On the Infinitude of Prime Elements

Acerca de la infinitud de elementos primos

LUIS F. CÁCERES-DUQUE1, JOSÉ A. VÉLEZ-MARULANDA2

1University of Puerto Rico at Mayagüez, Mayagüez, PR, USA. Email: luis.caceres1@upr.edu
2Valdosta State University, Valdosta, GA, USA. Email: javelezmarulanda@valdosta.edu


Abstract

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).

Key words: Unique factorization domains, Prime elements.


2000 Mathematics Subject Classification: 11A41, 13G99.

Resumen

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 R satisface 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).

Palabras clave: Dominios de factorización única, elementos primos.


Texto completo disponible en PDF


References

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(Recibido en mayo de 2013. Aceptado en julio de 2013)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv47n2a04,
    AUTHOR  = {Cáceres-Duque, Luis F. and Vélez-Marulanda, José A.},
    TITLE   = {{On the Infinitude of Prime Elements}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2013},
    volume  = {47},
    number  = {2},
    pages   = {167--179}
}