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Commutator-finite D-lattices. (English) Zbl 1081.06013
The author studies lattice-ordered D-posets (= D-lattices). She finds conditions when a commutator-finite D-lattice \(L\) can be uniquely decomposed in the form \(L \cong M\times L_1 \times \cdots\times L_n\), where \(M\) is an MV-algebra and \(L_1,\ldots,L_n\) are irreducible D-lattices which are not MV-algebras. The basic problem in question is the presence of so-called unsharp elements. In addition, she proves that the class of commutator-finite D-lattices contains, under some conditions, the class of block-finite D-lattices. This allows her to study some interesting questions concerning states and valuations.

MSC:
06D35 MV-algebras
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
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