## 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 $$P$$.

### MSC:

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