Convexity, Valuations and Prüfer Extensions in Real Algebra

We analyse the interplay between real valuations, Prüfer extensions and convexity with respect to various preorderings on a given commutative ring. We study all this first in preordered rings in general, then in $f$-rings. Most often Prüfer extensions and real valuations abound whenever a preordering is present. The next logical step, to focus on the more narrow class of real closed rings, is not yet taken, except in some examples.

2000 Mathematics Subject Classification: 13J30 (13A18, 13F05)

Keywords and Phrases: valuation, Prüfer extension, real holomorphy ring, convex subring

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