Let $\bar{\Kset}_f$ denote the commutative unital ring of Colombeau's full
generalized numbers. This ring can be endowed with an ultra-metric in such a
way that it becomes a topological ring. There are many interesting question
about $\bar{\Kset}_f$ in the framework of Commutative Algebra and General
Topology as well as of the superposition of these two subjects. The purpose of
this paper aims to give an initial step toward the study of this ring.