Order

, Volume 12, Issue 3, pp 295–305

Lattice uniformities and modular functions on orthomodular lattices

  • Hans Weber
Article

DOI: 10.1007/BF01111744

Cite this article as:
Weber, H. Order (1995) 12: 295. doi:10.1007/BF01111744

Abstract

It is shown that the lattice of all exhaustive lattice uniformities on an orthomodular latticeL is isomorphic to the centre of a natural completion (of a quotient) ofL, and is thus a complete Boolean algebra. This is applied to prove a decomposition theorem for exhaustive modular functions on orthomodular lattices, which generalizes Traynor's decomposition theorem [14].

Mathematics Subject Classifications (1991)

06C1506F30

Key words

Orthomodular latticeslattice uniformitiesmodular functionsdecompositions

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Hans Weber
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di UdineUdineItaly