Geodesic
Decomposition of Projections on Orthomodular Lattices(1)
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 263-267

Voir la notice de l'article provenant de la source Cambridge University Press

The set of projections in the BAER*-semigroup of hemimorphisms on an orthomodular lattice L can be partially ordered such that the subset of closed projections becomes an orthocomplemented lattice isomorphic to the underlying lattice L. The set of closed projections is identical with the set of Sasaki-projections on L (Foulis [2]). Another interesting class of (in general nonclosed) projections, first investigated by Janowitz [4], are the symmetric closure operators. They map onto orthomodular sublattices where Sasaki-projections map onto segments of the lattice L. 
Rüttimann, G. T. Decomposition of Projections on Orthomodular Lattices(1). Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 263-267. doi: 10.4153/CMB-1975-050-0
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[1] 1. Birkhoff, G., Lattice Theory, American Mathematical Society, 3rd ed. (1967). Google Scholar

[2] 2. Foulis, D. J., BAER*-Semigroups, Proceedings of the Amerian Mathematical Society 11, 648-654 (1960). Google Scholar

[3] 3. Foulis, D. J., A Note on Orthomodular Lattices, Portugaliae Mathematica 21, 65-72 (1962). Google Scholar

[4] 4. Janowitz, M. F., Residuated Closure Operators. Portugaliae Mathematica 26,221-252 (1967). Google Scholar

[5] 5. Nakamura, M., The Permutability in a Certain Orthocomplemented Lattice, Kodai Math. Sem. Rep. 9, 158-160 (1957). Google Scholar

[6] 6. Sasaki, U., On Orthocomplemented Lattices Satisfying the Exchange Axiom. Hiroshima Japan University Journal of Science Ser. A17, 293-302 (1954). Google Scholar

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