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Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras

Part of: Algebraic logic General logic

Published online by Cambridge University Press:  09 April 2009

Anatolij Dvurečenskij
Anatolij Dvurečenskij
Affiliation:
Mathematical InstituteSlovak Academy of Sciences Štefánikova 49 SK-814 73 Bratislava Slovakia e-mail: dvurecen@mat.savba.sk
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Abstract

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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.

Keywords

Pseudo-effect algebraeffect algebracentral elementgeneral comparabilitypseudo MV-algebramonotone σ-completenessCantor-Bernstein theorem

MSC classification

Secondary: 03G12: Quantum logic 03B50: Many-valued logic
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 1 , February 2003 , pp. 121 - 144
Copyright
Copyright © Australian Mathematical Society 2003

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