Real Algebraic and Analytic Geometry |

SV-Rings and SV-Porings.

e-mail:

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

Submission: 2008, October 8.

*Abstract:
SV-rings are commutative rings whose factor rings modulo prime
ideals are valuation rings. SV-rings occur most naturally in connection with
partially ordered rings (= porings) and have been studied only in this context
so far. The present note first develops the theory of SV-rings systematically,
without assuming the presence of a partial order. Particular attention is paid
to the question of axiomatizability (in the sense of model theory). Partially
ordered SV-rings (SV-porings) are introduced, and some elementary
properties are exhibited. Finally, SV-rings are used to study convex subrings
and convex extensions of porings, in particular of real closed rings.*

**Full text**, 30p.:
pdf 13680k.

Server Home Page