2009 | OriginalPaper | Chapter
Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas
Author : Konrad Schmüdgen
Published in: Emerging Applications of Algebraic Geometry
Publisher: Springer New York
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We propose and discuss how basic notions (quadratic modules, positive elements, semialgebraic sets, Archimedean orderings) and results (Positivstellensätze) from real algebraic geometry can be generalized to noncommutative *-algebras. A version of Stengle's Positivstellensatz for n X n matrices of real polynomials is proved.