Supertropical polynomials and resultants

摘要

This paper, a continuation of Izhakian and Rowen (in press) [5], involves a closer study of polynomials over supertropical semirings and their version of tropical geometry. We introduce the concept of relatively prime polynomials (in one indeterminate) and resultants, with the aid of some topology. Polynomials in one indeterminant are seen to be relatively prime iff they do not have a common tangible root, iff their resultant is tangible. Applying various morphisms of supertropical varieties leads to a supertropical version of Bézout's theorem.