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Surveying Lattice-Ordered Fields

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Ordered Algebraic Structures

Part of the book series: Developments in Mathematics ((DEVM,volume 7))

Abstract

The object of what follows is to give a brief overview of the theory of lattice-ordered fields. While I have included no proofs, I have tried to give ample references for anyone interested in seeing the details. Section 1 briefly sketches the history behind the subject and section 2 recalls some basic definitions. The remainder reviews what is presently known: section 3 describes methods of constructing lattice-ordered fields; section 4 concerns the maximal totally ordered subfield; section 5 considers lattice-ordered fields as vector lattices; section 6 describes representations of lattice-ordered fields by means of power series fields; section 7 discusses the number of different compatible lattice orderings; section 8 deals with extensions to total orders; section 9 investigates the lattice-ordering of simple algebraic extensions of totally ordered fields; and section 10 lists some open questions. Of course not all results are mentioned below. I have chosen those that seem to me to be the most fundamental and the most interesting.

I have cited specific results in one of two ways: if an author has given the n th result in the m th section the number m.n, then I have used that number; otherwise, I have used the number of the page on which the result occurs.

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Authors and Affiliations

  1. Department of Mathematics, Hamilton College, Clinton, NY, 13323, USA

    R. H. Redfield

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Editors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Jorge Martínez

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© 2002 Springer Science+Business Media Dordrecht

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Redfield, R.H. (2002). Surveying Lattice-Ordered Fields. In: Martínez, J. (eds) Ordered Algebraic Structures. Developments in Mathematics, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3627-4_6

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  • DOI: https://doi.org/10.1007/978-1-4757-3627-4_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5225-7

  • Online ISBN: 978-1-4757-3627-4

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