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A Priestley-type Method for Generating Free l-Groups

  • Néstor G. Martínez
  • Alejandro Petrovich
Part of the Developments in Mathematics book series (DEVM, volume 7)

Abstract

A Priestley-type topological representation is developed for the class of partially ordered groups which are p. o. subgroups of lattice-ordered groups. The appropriated analog of the spectrum of prime lattice filters is the class of increasing subsets P satisfying abP and cdP imply adP or cbP. In developing this representation, we give new embedding theorems for these groups. In particular, we give a necessary and sufficient condition for a p. o. group in this class to be embedded in an l-group of sets in such a way that the embedding preserves meets and joins that already exist in the group. Our construction gives also an alternative and very natural way to obtain the free l-group generated by a p. o. group in this class.

Keywords

Distributive Lattice Positive Cone Opposite Inclusion Complete Family Priestley Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Néstor G. Martínez
    • 1
  • Alejandro Petrovich
    • 1
  1. 1.Departamento de MatemdticaUniversidad de Buenos AiresBuenos AiresArgentina

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