Boolean Metric Spaces and Boolean Algebraic Varieties.

The concepts of Boolean metric space and convex combination are used to characterize polynomial maps An → Am in a class of commutative Von Neumann regular rings including p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e., sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces. [ABSTRACT FROM AUTHOR]