Lattice-ordered fields

DOI10.1007/BF00390108zbMath0603.06009MaRDI QIDQ1082357

Niels Schwartz

Publication date: 1986

Published in: Order (Search for Journal in Brave)

zbMATH Keywords

total orderpartially ordered vector spacealgebraic field extensionarchimedean l-fieldsarchimedean lattice-ordered fieldsstructure of the additive l-group

Mathematics Subject Classification ID

Algebraic field extensions (12F05) Arithmetic theory of polynomial rings over finite fields (11T55) Ordered rings, algebras, modules (06F25) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Ordered fields (12J15)

Related Items (13)

Directed partial orders over non-Archimedean \(o\)-fields ⋮ On the existence of directed rings and algebras with negative squares ⋮ Lattice-ordered fields determined by \(d\)-elements ⋮ Internal characterizations of lattice-ordered power series fields ⋮ Some questions on partially ordered rings – a survey ⋮ Non-Archimedean directed fields \(K(i)\) with o-subfield \(K\) and \(i^2=-1\). ⋮ Note on classification of two-dimensional associative lattice-ordered real algebras ⋮ Fields with directed partial orders ⋮ Lattice-ordered fields as convolution algebras ⋮ Subfields of Lattice-Ordered Fields That Mimic Maximal Totally Ordered Subfields ⋮ Matrix ℓ-algebras over ℓ-fields ⋮ Hereditary ℓ-ideals of matrix rings over ℓ-rings ⋮ Note on Lattice-ordered Rings with Positive Squares

Cites Work

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• Lattice orderings on the real field
• A embedding theorem for lattice-ordered fields
• The ring of polar preserving endomorphisms of an abelian lattice-ordered group
• Some Structure Theorems for Lattice-Ordered Groups
• Unique Representation of Archimedean Lattice Groups and Normal Archimedean Lattice Rings
• Sur les endomorphismes conservant les polaires d'un groupe réticulé archimédien

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