Abstract
Pseudo-effect algebras are partial algebras (E;+,0,1) with a partially defined addition + which is not necessarily commutative and therefore with two complements, left and right. If they satisfy a special kind of the Riesz decomposition property, they are intervals in unital po-groups. The general comparability property in unital po-groups with strong unit (G,u), allows to compare elements of G in some intervals with Boolean ends. Such a po-group is always an ℓ-group admitting a state. We prove that every such (G,u) is a subdirect product of linearly ordered unital po-groups.
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Dvurečenskij, A. Unital Groups and General Comparability Property. International Journal of Theoretical Physics 43, 2169–2185 (2004). https://doi.org/10.1023/B:IJTP.0000049017.10289.0b
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DOI: https://doi.org/10.1023/B:IJTP.0000049017.10289.0b