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Archimedean lattices

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Abstract

Anarchimedean lattice is a complete algebraic latticeL with the property that for each compact elementc∈L, the meet of all the maximal elements in the interval [0,c] is 0.L ishyper-archimedean if it is archimedean and for eachx∈L, [x, 1] is archimedean. The structure of these lattices is analysed from the point of view of their meet-irreducible elements. If the lattices are also Brouwer, then the existence of complements for the compact elements characterizes a particular class of hyper-archimedean lattices.

The lattice ofl-ideals of an archimedean lattice ordered group is archimedean, and that of a hyper-archimedean lattice ordered group is hyper-archimedean. In the hyper-archimedean case those arising as lattices ofl-ideals are fully characterized.

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Authors and Affiliations

  1. University of Florida, Gainesville, Florida, USA

    J. Martinez

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  1. J. Martinez
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Martinez, J. Archimedean lattices. Algebra Univ. 3, 247–260 (1973). https://doi.org/10.1007/BF02945124

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  • DOI: https://doi.org/10.1007/BF02945124

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