Supertropical Polynomials and Resultants

This paper, a continuation of [3], involves a closer study of polynomials of supertropical semirings and their version of tropical geometry in which we introduce the concept of relatively prime polynomials 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. The Frobenius property yields a morphism of supertropical varieties; this leads to a supertropical version of B\'ezout's theorem. Also, a supertropical variant of factorization is introduced which yields a more comprehensive version of Hilbert's Nullstellensatz than the one given in [3].