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@article{1368661,
author = {Niederle, Josef and Paseka, Jan},
article_location = {BERLIN},
article_number = {2},
doi = {http://dx.doi.org/10.1515/ms-2015-0140},
keywords = {non-classical logics; orthomodular lattices; effect algebras; MV-algebras; states; simplex algorithm},
language = {eng},
issn = {0139-9918},
journal = {Mathematica Slovaca},
title = {ON REALIZATION OF EFFECT ALGEBRAS},
volume = {66},
year = {2016}
}
TY - JOUR
ID - 1368661
AU - Niederle, Josef - Paseka, Jan
PY - 2016
TI - ON REALIZATION OF EFFECT ALGEBRAS
JF - Mathematica Slovaca
VL - 66
IS - 2
SP - 343-358
EP - 343-358
PB - Slovak Academy of Sciences
SN - 01399918
KW - non-classical logics
KW - orthomodular lattices
KW - effect algebras
KW - MV-algebras
KW - states
KW - simplex algorithm
N2 - 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(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(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. (C) 2016 Mathematical Institute Slovak Academy of Sciences
ER -
NIEDERLE, Josef and Jan PASEKA. ON REALIZATION OF EFFECT ALGEBRAS. \textit{Mathematica Slovaca}. BERLIN: Slovak Academy of Sciences, 2016, vol.~66, No~2, p.~343-358. ISSN~0139-9918. Available from: https://dx.doi.org/10.1515/ms-2015-0140.
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