Abstract

CACERES-DUQUE, LUIS F.  and  VELEZ-MARULANDA, JOSÉ A.. On the Infinitude of Prime Elements. Rev.colomb.mat. [online]. 2013, vol.47, n.2, pp.167-179. ISSN 0034-7426.

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 r∈ R with f(r)≠ 0, then either g=0 or \deg(f) ≤ \deg(g).

Keywords : Unique factorization domains; Prime elements.

        · abstract in Spanish     · text in English     · English ( pdf )