The structure group of a generalized orthomodular lattice
The author uses a dual definition of a generalized orthomodular lattice using axioms for the (upper) orthogonality relation and assuming the existence of a greatest element but not the existence of a least element. He characterizes generalized orthomodular lattices as singular \(L\)-algebras, shows that generalized orthomodular lattices correspond to orthomodular lattices with two-valued Jauch-Piron state. The main result states that there is a one-to-one correspondence between generalized orthomodular lattices and right \(\ell\)-groups of singular type (the correspondence is explicitly described).
scientific article; zbMATH DE number 6855868
scientific article