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Article

Chajda, Ivan
A groupoid characterization of orthomodular lattices. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 44 (2005), issue 1, pp. 13-18
MSC: 06C15, 20N02 | MR 2218563 | Zbl 1091.06006
Keywords:
orthomodular lattice; ortholattice; orthocomplementation; OML-algebra
Summary:
We prove that an orthomodular lattice can be considered as a groupoid with a distinguished element satisfying simple identities.
References:
[1] Abbott J. C.: Semi-boolean algebras. Matem. Vesnik, 4 (1967), 177–198. MR 0239957
[2] Birkhoff G.: Lattice Theory. : Proc. Amer. Math. Soc., Providence, R. I. third edition, 1967. MR 0227053
[3] Beran L.: Orthomodular Lattices – Algebraic Approach. : D. Reidel, Dordrecht. 1984. MR 0785005
[4] Chajda I.: A groupoid characterization of Boolean algebras. Discuss. Math., General algebra and appl., to appear. MR 2150654 | Zbl 1086.20041
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