algebra universalis

, Volume 8, Issue 1, pp 349–353

A universal mapping characterization of the completion by cuts

  • Alan A. Bishop
Article

Abstract

Closed maps of lattices are defined to be those satisfying the condition that the inverse image of closed ideals are closed ideas. Residuated maps are closed and closed maps are complete-join homomorphisms. The natural embeddingj of a lattice into its completion by cuts is a closed map. For every closed map ϕ from a latticeL into a complete latticeM, there exists a unique closed map φ* from the completion by cutsL intoM such that φ*j=φ. This characterizes the completion by cuts.

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References

  1. [1]
    G. Birkhoff,Lattice theory, Amer. Math. Soc. Coll. Publ.,25, New York, 1967.Google Scholar
  2. [2]
    T. S. Blyth, andM. F. Janowitz,Residuation theory, Pergamon Press (1972).Google Scholar
  3. [3]
    A. Bishop,A universal mapping property for a lattice completion, Algebra Universalis6 (1976). 81–84MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag 1978

Authors and Affiliations

  • Alan A. Bishop
    • 1
  1. 1.Western Illinois UniversityMacombUSA

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