Real closed rings
by
Niels Schwartz
University of Passau

Real closed rings occur in real algebraic geometry as rings of continuous semi-algebraic functions, in topology as rings of continuous functions with values in the reals, and in algebra as convex subrings of real closed fields. These convex subrings are known as real closed valuation rings. Real closed rings can be studied as partially ordered rings with radical relation (in the sense of Prestel and Schmid). This point of view leads to a particularly important role for real closed valuation rings. The lecture discusses their algebraic and model theoretic properties, as well as applications.

Date received: May 26, 1999