J. Aust. Math. Soc.  74 (2003), 121-143
Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras

Anatolij Dvurecenskij
  Mathematical Institute
  Slovak Academy of Sciences
  Stefánikova 49
  SK-814 73 Bratislava

Pseudo-effect algebras are partial algebras $(E;+,0,1)$ 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 $E$ satisfies general comparability, then $E$ 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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