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A universal mapping characterization of the completion by cuts

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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. G. Birkhoff,Lattice theory, Amer. Math. Soc. Coll. Publ.,25, New York, 1967.

  2. T. S. Blyth, andM. F. Janowitz,Residuation theory, Pergamon Press (1972).

  3. A. Bishop,A universal mapping property for a lattice completion, Algebra Universalis6 (1976). 81–84

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Authors and Affiliations

  1. Western Illinois University, Macomb, Illinois, USA

    Alan A. Bishop

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  1. Alan A. Bishop
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Bishop, A.A. A universal mapping characterization of the completion by cuts. Algebra Universalis 8, 349–353 (1978). https://doi.org/10.1007/BF02485405

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  • DOI: https://doi.org/10.1007/BF02485405

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