Real Algebraic and Analytic Geometry
Submission: 2008, October 8.
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.
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