SOME STRUCTURAL PROPERTIES OF THE TOPOLOGICAL RING OF COLOMBEAU'S GENERALIZED NUMBERS

Abstract

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