J. Aust. Math. Soc.
75 (2003), 295-311
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Infinitary lattice and Riesz properties of pseudoeffect algebras and po-groups
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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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Thomas Vetterlein
Mathematical Institute
Slovak Academy of Sciences
Stefánikova 49
SK -- 814 73 Bratislava
Slovakia
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.
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