Boolean Metric Spaces and Boolean Algebraic Varieties

Abstract

The concepts of Boolean metric space and convex combination are used to characterize polynomial maps A ⁿ  → A ^m 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.

Key Words:

• Boolean metric
• Boolean distance
• Algebraic variety
• Boolean domain

Mathematics Subject Classification:

• Primary 13AXX
• Secondary 06E30
• 16E50
• 51F99

Acknowledgments

The author wishes to thank Professors Juan Martínez and Manuel Saorín, of the University of Murcia, and Sergiu Rudeanu, of the University of Bucharest, for their support and stimulus, and for their help in the redaction of this article. He was supported by FPU grant of SEEU-MECD, Spain.

Notes

^#Communicated by R. Wisbauer.