algebra universalis

, Volume 3, Issue 1, pp 247–260 | Cite as

Archimedean lattices

  • J. Martinez


Anarchimedean lattice is a complete algebraic latticeL with the property that for each compact elementcL, the meet of all the maximal elements in the interval [0,c] is 0.L ishyper-archimedean if it is archimedean and for eachxL, [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.


Boolean Algebra Complete Lattice Algebra UNIV Universal Algebra Prime Element 
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Copyright information

© Birkhäuser-Verlag 1973

Authors and Affiliations

  • J. Martinez
    • 1
  1. 1.University of FloridaGainesvilleUSA

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