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Lattice-ordered fields

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Abstract

Mainly archimedean lattice-ordered fields (l-fields) are investigated in this paper. An archimedean l-field has a largest subfield (its o-subfield) which can be totally ordered in such a way that the l-field is a partially ordered vector space over this subfield. For archimedean l-fields which are algebraic over their o-subfields the following questions are investigated: What is the structure of the additive l-group of an l-field? Can the lattice order of an l-field be extended to a total order? Are the intermediate fields of an l-field and its o-subfield also l-fields with the induced partial order?

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstrasse 39, 8, Munich 2, West Germany

    Niels Schwartz

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  1. Niels Schwartz
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Communicated by K. Keimel

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Schwartz, N. Lattice-ordered fields. Order 3, 179–194 (1986). https://doi.org/10.1007/BF00390108

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  • DOI: https://doi.org/10.1007/BF00390108

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