DOCUMENTA MATHEMATICA, Vol. 10 (2005), 1-109

Manfred Knebusch and Digen Zhang

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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