Real Algebraic and Analytic Geometry
Submission: 2016, September 27.
We introduce positive cones on algebras with involution. These allow us to prove analogues of Artin's solution to Hilbert's 17th problem and the Artin-Schreier theorem characterizing formally real fields. We introduce the corresponding space of orderings of an algebra with involution and investigate its topological properties, showing in particular that it is a spectral space. As an application we solve the problem of the existence of positive involutions. .
Mathematics Subject Classification (2010): 13J30, 16K20, 11E39.
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