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

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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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     title = {Decomposition of {Projections} on {Orthomodular} {Lattices(1)}},
     journal = {Canadian mathematical bulletin},
     pages = {263--267},
     year = {1975},
     volume = {18},
     number = {2},
     doi = {10.4153/CMB-1975-050-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-050-0/}
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