Arithmetic and Polynomials over Fuzzy Rings

Abstract

Fuzzy rings are, on the one handside, an appropriate tool for a unified approach to representable, oriented, and valuated matroids. On the other hand, they also serve to unify the relatively new field of "Tropical Geometry" and "Classical Algebraic Geometry." Therefore, these fuzzy rings deserve a more thorough examination. We study the arithmetic in fuzzy rings and related structures as well as polynomials over these coefficient domains.