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.
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