3 Oct 2006

2:30 - 4:00    Niels Schwartz (University of Passau)

From rings of continuous functions to real closed rings

Abstract
Rings of continuous functions from topological spaces to the real
numbers are one of the most important tools in general topology. From
an algebraists point of view, they have some shortcomings: If basic
ring-theoretic constructions, such as factor rings or quotient rings,
are applied to rings of continuous functions then usually they do not
produce rings of continuous functions. Real closed rings form a
rather small category that contains all rings of continuous functions
and is closed under many ring-theoretic constructions. Real closed
rings are an elementary class (in the sense of model theory). They
establish a link between general topology and modern real algebraic
geometry.