Convexity, valuations and Prüfer extensions in real algebra.

Knebusch, Manfred; Zhang, Digen

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$S V$ -Rings and $S V$ -Porings

Niels Schwartz (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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$S V$ -rings are commutative rings whose factor rings modulo prime ideals are valuation rings. $S V$ -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of $S V$ -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered $S V$ -rings ( $S V$ -porings)...