The Noncommutative Graded Positivstellensatz

Abstract

In this article we give an abstract graded (homogeneous) Positivstellensatz for noncommutative rings. Later we prove a version of Lang's homomorphism theorem and use it to deduce a geometric version of the homogeneous Positivstellensatz.

Key Words:

• Positivstellensatz
• Orderings
• Lang's homorphism theorem
• Graded rings

Acknowledgments

The author is greatly indebted to Jaka Cimprič for suggesting the problem and for many stimulating conversations. This work was partially sponsored by the Ministry of Education, Science and Sport of Slovenia.

Notes

^#Communicated by A. Prestel.