Some structural properties of the topological ring of Colombeau's generalized numbers

Let (K) over bar denote the commutative ring with identity of Colombeau's g eneralized numbers. (K will denote either R or C). This ring can be endowed with an ultra-metric in such a way that (K) over bar is a topological ring . There are many interesting questions about (K) over bar in the frameworks of Commutative Algebra and General Topology as well as of the superpositio n of these two subjects. This paper is meant to represent an initial step i n this direction. In a few simple cases the study is extended to the ring o f Colombeau's generalized functions on an open subset of R-n.