Some Properties of Posynomial Rings

In this article we shall study some basic properties of posynomial rings with particular emphasis on rings $\mathrm{P}\mathrm{o}\mathrm{s}(K,\mathbb{Q})[\bar{x}]$, and ${\rm Pos}(K,$\mathbb{Z}$)[\bar x]$. The latter ring is the well known ring of Laurent polynomials.