J. Aust. Math. Soc.
74 (2003), 121-143
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Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras
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Anatolij Dvurecenskij
Mathematical Institute
Slovak Academy of Sciences
Stefánikova 49
SK-814 73 Bratislava
Slovakia
dvurecen@mat.savba.sk
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Abstract
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Pseudo-effect algebras are partial algebras
 with a partially defined addition
 which is not necessary commutative and with two
complements, left and right ones. We define
central elements of a pseudo-effect algebra and
the centre, which in the case of MV-algebras
coincides with the set of Boolean elements and in
the case of effect algebras with the Riesz
decomposition property central elements are only
characteristic elements. If
 satisfies general comparability, then
 is a pseudo MV-algebra. Finally, we apply
central elements to obtain a variation of the
Cantor-Bernstein theorem for pseudo-effect
algebras.
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