Displaying similar documents to “Discrete ordered rings”

On ordered division rings

Ismail M. Idris (2001)

Colloquium Mathematicae

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Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel's axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under x ↦ xa² for non-zero a, in place of requiring that positive elements have a positive product. Our aim in this work is to study this type of ordering in the case of a division ring. We show that it actually behaves just as...

On f -rings that are not formally real

James J. Madden (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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Henriksen and Isbell showed in 1962 that some commutative rings admit total orderings that violate equational laws (in the language of lattice-ordered rings) that are satisfied by all totally-ordered fields. In this paper, we review the work of Henriksen and Isbell on this topic, construct and classify some examples that illustrate this phenomenon using the valuation theory of Hion (in the process, answering a question posed in [E]) and, finally, prove that a base for the equational...

Some cardinal characteristics of ordered sets

Vítězslav Novák (1998)

Czechoslovak Mathematical Journal

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For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.