Generalization of blocks for \(D\)-lattices and lattice-ordered effect algebras. (English) Zbl 0968.81003

Summary: We show that every \(D\)-lattice (lattice-ordered effect algebra) \(P\) is a set-theoretic union of maximal subsets of mutually compatible elements, called blocks. Moreover, blocks are sub-\(D\)-lattices and sub-effect algebras of \(P\) which are \(MV\)-algebras closed with respect to all suprema and infima existing in \(P\).


81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
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