Pulmannová, Sylvia On connections among some orthomodular structures. (English) Zbl 0947.06004 Demonstr. Math. 30, No. 2, 313-328 (1997). From the introduction: By an orthomodular structure we mean a poset with (partially) defined operations \(\ominus,\oplus\) such that \(a\leq b\Rightarrow b=a\oplus(b\ominus a)\), which can be considered as a generalized form of orthomodular law. We study connections between the following orthomodular structures.Difference posets (effect algebras, alternatively), have been found a useful tool of pursuing quantum mechanical constructions. An important example of a \(D\)-poset is the set of all effects (i.e., s.a. operators \(A\) with \(0\leq A\leq I\) on a Hilbert space), which play an important role in unsharp quantum measurements.The notion of a commutative minimal clan as a common abstraction of Boolean rings and commutative lattice-ordered groups was introduced by Schmidt.The notion of an MV-algebra was introduced by Chang in 1957, where MV is supposed to suggest many-valued logic. According to Abbott, a meet semi-Boolean algebra is a meet semilattice in which every principal ideal is a Boolean algebra. Abbott has shown that meet semi-Boolean algebras are equationally defined as subtraction algebras.A close relation between effect algebras and semi-MV-algebras is shown. Cited in 5 Documents MSC: 06C15 Complemented lattices, orthocomplemented lattices and posets 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) Keywords:effect algebras; difference posets; orthomodular structure; minimal clan; MV-algebra; meet semi-Boolean algebra PDFBibTeX XMLCite \textit{S. Pulmannová}, Demonstr. Math. 30, No. 2, 313--328 (1997; Zbl 0947.06004)