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, Volume 6, Issue 2, pp 181–194 | Cite as

Commutators and decompositions of orthomodular lattices

  • Georges Chevalier
Article

Abstract

We show that in any complete OML (orthomodular lattice) there exists a commutatorc such that [0,c] is a Boolean algebra. This fact allows us to prove that a complete OML satisfying the relative centre property is isomorphic to a direct product [0,a] × [0,a] wherea is a join of two commutators, [0,a] is an OML without Boolean quotient and [0,a] is a Boolean algebra. The proof uses a new characterization of the relative centre property in complete OMLs. In a final section, we specify the previous direct decomposition in the more particular case of locally modular OMLs.

Key words

Orthomodular lattice commutator ideal of commutators relative centre property locally modular lattice 

AMS subject classifications (1980)

Primary 06C15 secondary 06B10 

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Georges Chevalier
    • 1
  1. 1.Institut de Mathématiques et InformatiqueUniversité Lyon 1France

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