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

Loading next page...
 
/lp/springer_journal/positivity-and-convexity-in-rings-of-fractions-v0vFrBEXZI
Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2007 by Birkhäuser Verlag, Basel
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

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations
Access to DeepDyve database
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off