# Positivity and Convexity in Rings of Fractions

Positivity and Convexity in Rings of Fractions 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 +. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Positivity and Convexity in Rings of Fractions

Positivity, Volume 11 (4) – Sep 26, 2007
48 pages

/lp/springer_journal/positivity-and-convexity-in-rings-of-fractions-v0vFrBEXZI
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-007-2077-7
Publisher site
See Article on Publisher Site

### 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 +.

### Journal

PositivitySpringer Journals

Published: Sep 26, 2007

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