Abstract
An orthomodular lattice is constructed by taking a homomorphic image of the ortholattice obtained from a certain orthogonality relation on an infinite set.
Similar content being viewed by others
References
Birkhoff, G.,Lattice Theory. Colloquium Publications25. American Math Society, Providence, Rhode Island 1984.
Bruns, G.,A finiteness criterion for onhomodular lattices. Canadian Journal of MathematicsXXX (1978), 315–320.
Bruns, G. andGreechie, R. J.,Blocks and commutators in orthomodular lattices. Algebra Universalis27 (1990), 1–9.
Foulis, D. J. andRandall, C. H.,Lexicographic orthogonality. J. Combinatorial Theory11 (1971), 157–162.
Greechie, R. J.,On the structure of orthomodular lattices satisfying the chain condition. J. Combinatorial Theory4 (1968), 210–219.
Greechie, R. J.,On generating pathological orthomodular structures. Kansas State Univ. Technical Report 13, 1970.
Greechie, R. J.,Orthomodular lattices admitting no states. J. Combinatorial Theory10 (1971), 119–132.
Greechie, R. J. andHerman, L.,Commutator-finite orthomodular lattices. Order1 (1985), 277–284.
Holland Jr., S. S.,The current interest in orthomodular lattices, in: J. C. Abbott (ed.),Trends in Lattice Theory, van Nostrand, 1970, pp. 41–126.
Huhn, A. P.,Schwach distributive Verbände I. Acta Sci. Math.33 (1972), 297–305.
Kalmbach, G.,Orthomodular Lattices. Academic Press, New York, 1983.
Mayet, R. andRoddy, M.,n-Distributivity in ortholattices, in:Contributions to General Algebra 5, Proceedings of the Salzburg Conference, May 29–June 1, 1986, 285–294, 1987.
Roddy, M.,An orthomodular analogue of the Birkhoff-Menger theorem. Algebra Universalis19 (1984), 55–60.
Sierpinski, W.,Sur un décomposition d'ensembles. Monatsh. Math.35 (1928), 239–248.
Author information
Authors and Affiliations
Additional information
This research was supported by N.S.E.R.C. grant 0041702.
Rights and permissions
About this article
Cite this article
Roddy, M.S. An orthomodular lattice. Algebra Universalis 29, 564–579 (1992). https://doi.org/10.1007/BF01190782
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01190782