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A Cantor-Bernstein type theorem for effect algebras. (English) Zbl 1061.06020
Effect algebras were introduced by D. J. Foulis and M. K. Bennet in 1994. An effect algebra is a partial groupoid with two constants $$0$$ and $$1$$ such that the partial binary operation $$\oplus$$ is associative, commutative, for each $$a$$ there is a unique $$a{'}$$ with $$a \oplus a{'} = 1$$ and if $$a \oplus 1$$ exists then $$a = 0$$. It is proved that if $$E_{1}$$ and $$E_{2}$$ are $$\sigma$$-complete effect algebras such that $$E_{1}$$ is a direct factor of $$E_{2}$$ and vice versa, then $$E_{1},E_{2}$$ are isomorphic.

##### MSC:
 06C15 Complemented lattices, orthocomplemented lattices and posets 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
##### Keywords:
Cantor-Bernstein theorem; effect algebra; weak congruence
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