Commutators in Orthomodular Lattices
Copyright policy )Commutators in Orthomodular Lattices
The author introduces the notions of a ''commutator'' for a possibly infinite set of elements M of an orthomodular lattice L and ''partial compatible'' (p.c.) for M with respect to some element \(a\in C(M)\) such that \(\{\) \(m\wedge a|\) \(m\in M\}\) is Boolean. If M is p.c. for \(a\in L\) then \(a\leq com(M)\) and CC(M) is p.c. for a; \(\{\) \(x\in L|\) x p.c. for \(a\}\) are orthomodular sublattices of L. These results are applied to commutators of observables.
Complemented lattices, orthocomplemented lattices and posets, commutators of observables, orthomodular lattice, commutator, partial compatible, Structure theory of lattices
Complemented lattices, orthocomplemented lattices and posets, commutators of observables, orthomodular lattice, commutator, partial compatible, Structure theory of lattices
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