Real Algebraic and Analytic Geometry
Submission: 2007, May 31.
Given a commutative ring $A$ equipped with a preordering $A^+$ (in the most general sense, see below), we look for a fractional ring extension (= ``ring of quotients'' in the sense of Lambek et al. [L]) as big as possible such that $A^+$ extends to a preordering $R^+$ of $R$ (i.e. with $A \cap R^+ = A^+$) in a natural way. We then ask for subextensions $A \subset B$ of $A \subset R$ such that $A$ is convex in $B$ with respect to $B^+ := B \cap R^+$.
Mathematics Subject Classification (2000): 13J25, 13J30, 13F05.
Keywords and Phrases: preordered ring extension, positively dense set, convexity cover, positivity divisor, convexity divisor.
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