Real Algebraic and Analytic Geometry
Submission: 2003, September 16.
In this paper we give a general theorem that describes necessary and sufficient conditions for a module to satisfy the so--called Kadison--Dubois property. This is used to generalize Jacobi's version of the Kadison--Dubois representation to associative rings. We apply this representation to obtain a noncommutative algebraic and geometric version of Putinar's Positivstellensatz. We finish the paper by answering questions given by Marshall and Jacobi.
Mathematics Subject Classification (2000): 12D15, 14P10, 06F25.
Full text, 10p.: dvi 45k, ps.gz 160k, pdf 195k.