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Displaying similar documents to “On f -rings that are not formally real”

Non-transitive generalizations of subdirect products of linearly ordered rings

Jiří Rachůnek, Dana Šalounová (2003)

Czechoslovak Mathematical Journal

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Weakly associative lattice rings (wal-rings) are non-transitive generalizations of lattice ordered rings (l-rings). As is known, the class of l-rings which are subdirect products of linearly ordered rings (i.e. the class of f-rings) plays an important role in the theory of l-rings. In the paper, the classes of wal-rings representable as subdirect products of to-rings and ao-rings (both being non-transitive generalizations of the class of f-rings) are characterized and the class of wal-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...

Introduction

Charles N. Delzell, James J. Madden (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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