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Lattice-ordered Fields Determined by d-elements

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Abstract

Most results on the structure of lattice-ordered fields require that the field have a positive multiplicative identity. We construct a functor from the category of lattice-ordered fields with a vector space basis of d-elements to the full subcategory of such fields with positive multiplicative identities. This functor is a left adjoint to the forgetful functor and, in many cases, allows us to write all compatible lattice orders in terms of orders with positive multiplicative identities. We also use these results to characterize algebraically those extensions of totally ordered fields that have vℓ-bases of d-elements.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston at Clear Lake, 2700 Bay Area Boulevard, Houston, TX, 77058, USA

    Jingjing Ma

  2. Department of Mathematics, Hamilton College, 198 College Hill Road, Clinton, NY, 13323, USA

    R. H. Redfield

Authors
  1. Jingjing Ma
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  2. R. H. Redfield
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Correspondence to R. H. Redfield.

Additional information

This paper is dedicated to Bernhard Banaschewski on the occasion of his 80th birthday.

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Ma, J., Redfield, R.H. Lattice-ordered Fields Determined by d-elements. Appl Categor Struct 15, 19–33 (2007). https://doi.org/10.1007/s10485-007-9063-x

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  • DOI: https://doi.org/10.1007/s10485-007-9063-x

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