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Infinitary lattice and Riesz properties of pseudoeffect algebras and po-groups

Part of: Ordered structures Algebraic logic

Published online by Cambridge University Press:  09 April 2009

Anatolij Dvurečenskij  and
Thomas Vetterlein
Anatolij Dvurečenskij
Affiliation:
Mathematical InsituteSlovak Academy of SciencesŠtef´nikova 49, SK - 814 73 Bratislava Slovakia, e-mail: dvurecen@mat.savba.sk vetterl@mat.savba.sk
Thomas Vetterlein
Affiliation:
Mathematical InsituteSlovak Academy of SciencesŠtef´nikova 49, SK - 814 73 Bratislava Slovakia, e-mail: dvurecen@mat.savba.sk vetterl@mat.savba.sk
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Abstract

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Pseudoeffect (PE-) algebras generalize effect algebras by no longer being necessarily commutative. They are in certain cases representable as the unit interval of a unital po-group, for instance if they fulfil a certain Riesz property.

Several infinitary lattice properties and the countable Riesz interpolation property are studied for PE-algebras on the one hand and for po-groups on the other hand. We establish the exact relationships between the various conditions that are taken into account, and in particular, we examine how properties of a PE-algebra are related to the analogous properties of a representing po-group.

Keywords

pseudoeffect algebraspo-groupsσ-complete PE-algebrasmonotone σ- complete PE-algebrasorthogonally σ-complete PE-algebrasPE-algebras with countable Riesz interpolation

MSC classification

Secondary: 81P10: Logical foundations of quantum mechanics; quantum logic 06F15: Ordered groups 03G12: Quantum logic

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 3 , December 2003 , pp. 295 - 312
Copyright
Copyright © Australian Mathematical Society 2003

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