J. Aust. Math. Soc.
74 (2003), 121143

Central elements and CantorBernstein's theorem for pseudoeffect algebras

Anatolij Dvurecenskij
Mathematical Institute
Slovak Academy of Sciences
Stefánikova 49
SK814 73 Bratislava
Slovakia
dvurecen@mat.savba.sk



Abstract

Pseudoeffect 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 pseudoeffect algebra and
the centre, which in the case of MValgebras
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 MValgebra. Finally, we apply
central elements to obtain a variation of the
CantorBernstein theorem for pseudoeffect
algebras.

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