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Morphisms and pasting of orthoalgebras. (English) Zbl 1057.81005
The Greechie’s constructions for pasting orthomodular lattices are extended for orthoalgebras. The author first shows how orthoalgebra monomorphisms and epimorphisms ought to be defined. Then she shows that the pasting of any two disjoint orthoalgebras along corresponding sections is an orthoalgebra. This orthoalgebra is an orthomodular poset if it is the pasting of orthomodular posets.

##### MSC:
 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 06C15 Complemented lattices, orthocomplemented lattices and posets
##### Keywords:
orthoalgebra; morphisms
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##### References:
 [1] DICHTL M.: Astroids and pastings. Algebra Universalis 18 (1985), 380-385. · Zbl 0546.06007 [2] FOULIS D. J.-GREECHIE R. J.-RÜTTIMANN G. T.: Filters and supports. Internat. J. Theoret. Phys. 31 (1992), 789-807. · Zbl 0764.03026 [3] GREECHIE R. J.: Orthomodular Lattices. Ph.D. Dissertation, University of Florida, 1966. · Zbl 0219.06007 [4] GREECHIE R. J.: On the structure of orthomodular lattices satisfying the chain condition. J. Combin. Theory 4 (1968), 210-218. · Zbl 0157.03703 [5] GREECHIE R. J.: Orthomodular lattices admitting no states. J. Combin. Theory 10 (1971), 119-132. · Zbl 0219.06007 [6] GUDDER S. P.: Quantum Probability. Academic Press, London-New York, 1986. [7] HABIL E. D.: Orthoalgebras and Noncommutative Measure Theory. Ph.D. Dissertation, Kansas State University, 1993. [8] KALMBACH G.: Orthomodular Lattices. Academic Press, London-New York, 1983. · Zbl 0528.06012 [9] NAVARA M.-ROGALEWICZ V.: The pasting construction for orthomodular posets. Math. Nachr. 154 (1991), 157-168. · Zbl 0767.06009 [10] RÜTTIMANN G. T.: The approximate Jordan-Hahn decomposition. Canad. J. Math. 41 (1989), 1124-1146. · Zbl 0699.28001
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