Displaying similar documents to “Ordered Rings and Fields”

Introduction

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

Annales de la faculté des sciences de Toulouse Mathématiques

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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...

Super real closed rings

Marcus Tressl (2007)

Fundamenta Mathematicae

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A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed...