Real Algebraic and Analytic Geometry
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209. Manfred Knebusch:
Positivity and convexity in rings of fractions.

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Submission: 2007, May 31.

Abstract:
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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