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

Colombeau's Algebra of full Generalized Numbers