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Finite homogeneous and lattice ordered effect algebras. (English) Zbl 1031.03078

Summary: We prove that for every finite homogeneous effect algebra \(E\) there exists a finite orthoalgebra \(O(E)\) and a surjective full morphism \(\phi_E : O(E)\to E\). If \(E\) is lattice-ordered, then \(O(E)\) is an orthomodular lattice. Moreover, \(\phi_E\) preserves blocks in both directions: the (pre)image of a block is always a block.

MSC:

03G12 Quantum logic
06C15 Complemented lattices, orthocomplemented lattices and posets
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