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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 a Jan PASEKA. ON REALIZATION OF EFFECT ALGEBRAS. \textit{Mathematica Slovaca}. BERLIN: Slovak Academy of Sciences, 2016, roč.~66, č.~2, s.~343-358. ISSN~0139-9918. Dostupné z: https://dx.doi.org/10.1515/ms-2015-0140.
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