Soft Computing

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

Lexicographic pseudo effect algebras

  • Anatolij DvurečenskijEmail author


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.


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 



This study was funded by the Grant VEGA No. 2/0069/16 SAV and GAČR 15-15286S.

Compliance with ethical standards

Conflicts of interest

Author declares that he has no conflict of interest.

Human participants or animals

This article does not contain any studies with human participants or animals performed by the author.


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© 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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