A general representation theorem for partially ordered commutative rings (Q1433408)

In this article the author proves a generalization of the classical Kadison-Dubois theorem that includes the classical version given by Becker and Schwartz as well, as the preordering version given by Jacobi. The main result is theorem 2.3 stating: Let \(A\) be a commutative ring with \(1\), \(T\) a weakly torsion preprime in \(A\) and \(M\) an Archimedean \(T\)-module. Then \(M\) satisfies the Kadison-Dubois property. The other main result is a generalized representation theorem (3.1). Applying these results to the ring \(A= \mathbb{R}[X]\) the author obtains a representation theorem for strictly positive polynomials and is able to sharpen various results of Jacobi and Prestel.