Representation of real commutative rings

During the last 10 years there have been several new results on the representation of real polynomials, positive on some semi-algebraic subset of . These results started with a solution of the moment problem by Schmüdgen for compact semi-algebraic sets. Later, Wörmann realized that the same results could be obtained by the so-called “Kadison–Dubois” Representation Theorem. The aim of our paper is to present this representation theorem together with its history, and to discuss its implication to the representation of positive polynomials. Also recent improvements of both topics by T. Jacobi and the author will be included.