Real Algebraic and Analytic Geometry |

Real closed valuation rings.

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homepage: http://www.fim.uni-passau.de/de/fim/fakultaet/lehrstuehle/algebraische-geometrie.html

Submission: 2008, October 8.

*Abstract:
The real closed valuation rings, i.e., convex subrings of real closed fields,
form a proper subclass of the class of real closed domains. It is shown how
one can recognize whether a real closed domain is a valuation ring. This
leads to a characterization of the totally ordered domains whose real closure
is a valuation ring. Real closures of totally ordered factor rings of coordinate
rings of real algebraic varieties are very frequently valuation rings. In
particular, the real closure of the coordinate ring of a curve is an SV-ring
(i.e., the factor rings modulo prime ideals are valuation rings). Real closed
valuation rings play a role in the definition of real closed rings, as well as in
the construction of real closures of rings and porings. They can also be used
for the study of univariate differentiable semi-algebraic functions. This
leads to the notion of differentiablility of semi-algebraic functions along
half branches of curves.*

**Full text**, 19p.:
pdf 7332k.

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