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

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.

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.

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