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Lattice uniformities and modular functions on orthomodular lattices

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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].

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  1. Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, I-33100, Udine, Italy

    Hans Weber

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  1. Hans Weber
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Communicated by K. Keimel

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Weber, H. Lattice uniformities and modular functions on orthomodular lattices. Order 12, 295–305 (1995). https://doi.org/10.1007/BF01111744

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