Modular almost orthogonal quantum logics
An orthomodular lattice (OML) is said to be almost orthogonal if it is atomic and if for every atom \(a\) in \(L\) the set \(B_ a=\{b\in L\mid b\) is an atom in \(L\) and \(b\not\leq a'\}\) is finite. Relations between almost orthogonality and modularity are studied. An almost orthogonal OML is modular if and only if it can be embedded into a direct product of finite modular quantum logics. The class of almost orthogonal modular OMLs is the largest subclass of the class of atomic modular OMLs in which the conditions commutator-finite and block-finite are equivalent.
scientific article; zbMATH DE number 95361