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The inheritance of BDE-property in sharply dominating lattice effect algebras and \((o)\)-continuous states. (English) Zbl 1247.03135
An effect algebra is a partial algebra with a commutative partial operation \(+\) of addition, which was introduced by D. J. Foulis and M. K. Bennett [Found. Phys. 24, No. 10, 1331–1352 (1994; Zbl 1213.06004)] and can model quantum-mechanical measurements.
The main subject of the paper under review is some important substructures of Archimedean atomic lattice effect algebras like blocks, the set of sharp elements, center, etc. The main results are: (i) For every sharply dominating Archimedean atomic lattice effect algebra, every atomic block is gain sharply dominating, and every of its elements can be decomposed, i.e., it has the so-called basic decomposition property (BDP). (ii) The state smearing theorem for compactly generated Archimedean atomic lattice effect algebras is proved.

MSC:
03G12 Quantum logic
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