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The center of an effect algebra. (English) Zbl 0846.03031
Summary: An effect algebra is a partial algebra modeled on the standard effect algebra of positive self-adjoint operators dominated by the identity on a Hilbert space. Every effect algebra is partially ordered in a natural way, as suggested by the partial order on the standard effect algebra. An effect algebra is said to be distributive if, as a poset, it forms a distributive lattice. We define and study the center of an effect algebra, relate it to cartesian-product factorizations, determine the center of the standard effect algebra, and characterize all finite distributive effect algebras as products of chains and diamonds.

MSC:
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
08A55 Partial algebras
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