The geometric shape and convexity of finitely generated module over ℝ+

Based on the basic theory of quasi-domains, the concept of nonnegative real number algebra is given in this paper. And the geometric shape and convexity of finitely generated module over nonnegative real number algebra are studied. We analyze the geometric shape of finitely generated module over nonnegative real number algebra with different dimensions and numbers of generating vector, and prove that they are all convex sets. At the end of this paper, the algebraic structure and the geometric shape of the finitely generated module over nonnegative real number algebra are compared with max-plus algebra.