Positivity and convexity in rings of fractions

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 boolean AND R+ = A(+)) in a natural way. We then ask for subextensions A C B of A C R such that A is convex in B with respect to B+ := B boolean AND R+.