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 ∩ R+ = A+) in a natural way. We then ask for subextensions A ⊂ B of A ⊂ R such that A is convex in B with respect to B+ : = B ∩ R+.
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A short form of this article has been delivered at the conference Carthapos 2006 at Carthago (Tunisia).
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Knebusch, M. Positivity and Convexity in Rings of Fractions. Positivity 11, 639–686 (2007). https://doi.org/10.1007/s11117-007-2077-7
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DOI: https://doi.org/10.1007/s11117-007-2077-7