Boolean metric spaces and Boolean algebraic varieties
Antonio Avil\'es

TL;DR
This paper introduces Boolean metric spaces and algebraic varieties over certain rings, establishing a correspondence that simplifies the study of polynomial solutions in these algebraic structures.
Contribution
It defines CFG-spaces and demonstrates their equivalence to algebraic varieties over CFG-rings, advancing the understanding of polynomial maps in these rings.
Findings
Boolean metric spaces characterize polynomial maps in CFG-rings
Algebraic varieties correspond to CFG-spaces in these rings
The study of polynomial solutions reduces to Boolean metric space analysis
Abstract
The concepts of Boolean metric space and convex combination are used to characterize polynomial maps in a class of commutative Von Neumann regular rings including Boolean rings and 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.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topology and Set Theory · Commutative Algebra and Its Applications
