Abstract
We characterize effect algebras and pseudo effect algebras that can be represented as an interval of the lexicographic product of an antilattice unital po-group (H, u) with a directed po-group G, both with the Riesz Decomposition Property (RDP). We show that a crucial condition is the existence of a lexicographic normal ideal. Finally, we present a categorical equivalence of the category of (H, u)-lexicographic pseudo effect algebras having RDP with the category of directed po-groups with RDP. In addition, a weaker form of the (H, u)-lexicographic pseudo effect algebra is studied.
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This study was funded by the Grant VEGA No. 2/0069/16 SAV and GAČR 15-15286S.
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Dvurečenskij, A. Lexicographic pseudo effect algebras. Soft Comput 21, 4981–4994 (2017). https://doi.org/10.1007/s00500-016-2228-5
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DOI: https://doi.org/10.1007/s00500-016-2228-5