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On realization of effect algebras

In: Mathematica Slovaca, vol. 66, no. 2
Josef Niederle - Jan Paseka
Detaily:
Rok, strany: 2016, 343 - 358
Kľúčové slová:
non-classical logics, orthomodular lattices, effect algebras, MV-algebras, states, simplex algorithm
O článku:
A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the lattice $L(\mathcal{H})$ of all closed subspaces of a separable complex Hilbert space. We show that a finite generalized effect algebra is order embeddable into the standard effect algebra $E({\mathcal H})$ of effects of a separable complex Hilbert space iff it has an order determining set of generalized states iff it is order embeddable into the power of a finite MV-chain. As an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it.
Ako citovať:
ISO 690:
Niederle, J., Paseka, J. 2016. On realization of effect algebras. In Mathematica Slovaca, vol. 66, no.2, pp. 343-358. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0140

APA:
Niederle, J., Paseka, J. (2016). On realization of effect algebras. Mathematica Slovaca, 66(2), 343-358. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0140
O vydaní:
Publikované: 1. 4. 2016