Geodesic
Convexity, valuations and Prüfer extensions in real algebra
Documenta mathematica, Tome 10 (2005), pp. 1-109
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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.
DOI : 10.4171/dm/183
Classification : 13A18, 13F05, 13J30
Mots-clés : valuation, Prüfer extension, real holomorphy ring, convex subring 
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     author = {Digen Zhang and Manfred Knebusch},
     title = {Convexity, valuations and {Pr\"ufer} extensions in real algebra},
     journal = {Documenta mathematica},
     pages = {1--109},
     year = {2005},
     volume = {10},
     doi = {10.4171/dm/183},
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Digen Zhang; Manfred Knebusch. Convexity, valuations and Prüfer extensions in real algebra. Documenta mathematica, Tome 10 (2005), pp. 1-109. doi: 10.4171/dm/183

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