caa a22 4500 445813741 CHVBK 20180317145219.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s11083-010-9191-z doi (NATIONALLICENCE)springer-10.1007/s11083-010-9191-z Subalgebras of Orthomodular Lattices [Elektronische Daten] [John Harding, Mirko Navara] Sachs (Can J Math 14:451-460, 1962) showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundations of quantum mechanics initiated by Butterfield and Isham (Int J Theor Phys 37(11):2669-2733, 1998, Int J Theor Phys 38(3):827-859, 1999), at least in the case where L is the orthomodular lattice of projections of a Hilbert space, or von Neumann algebra. The results here may add some additional perspective to this line of work. Springer Science+Business Media B.V., 2010 Orthomodular lattice nationallicence Subalgebra nationallicence Boolean nationallicence Harding John Department of Mathematical Sciences, New Mexico State University, 88003, Las Cruces, NM, USA aut Navara Mirko Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická2, 16627, Praha, Czech Republic aut Order Springer Netherlands 28/3(2011-11-01), 549-563 0167-8094 28:3<549 2011 28 11083 https://doi.org/10.1007/s11083-010-9191-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11083-010-9191-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Harding John Department of Mathematical Sciences, New Mexico State University, 88003, Las Cruces, NM, USA aut NATIONALLICENCE 700 1- Navara Mirko Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická2, 16627, Praha, Czech Republic aut NATIONALLICENCE 773 0- Order Springer Netherlands 28/3(2011-11-01), 549-563 0167-8094 28:3<549 2011 28 11083 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer