Soft Computing

, Volume 21, Issue 17, pp 4981–4994 | Cite as

Lexicographic pseudo effect algebras

Foundations
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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 (Hu) 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 (Hu)-lexicographic pseudo effect algebras having RDP with the category of directed po-groups with RDP. In addition, a weaker form of the (Hu)-lexicographic pseudo effect algebra is studied.

Keywords

Effect algebra Pseudo effect algebra The Riesz Decomposition Property Po-group Strong unit Lexicographic product Retractive ideal Lexicographic ideal Antilattice \((H, u)\)-perfect effect algebra Lexicographic effect algebra Strongly \((H, u)\)-perfect effect algebra 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia
  2. 2.Department of Algebra and GeometryPalacký UniversityOlomoucCzech Republic

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