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International Journal of Theoretical Physics

, Volume 53, Issue 5, pp 1685–1696 | Cite as

Some Remarks on Kite Pseudo Effect Algebras

  • Anatolij Dvurečenskij
  • W. Charles Holland
Article

Abstract

Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group G, a set I and with two bijections λ,ρ:II. Using a clever construction on the ordinal sum of (G +) I and (G ) I , we can define a pseudo effect algebra which can be non-commutative even if G is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.

Keywords

Pseudo MV-algebra Pseudo effect algebra -group Po-group Strong unit Kite pseudo effect algebra Subdirect product Po-loop 

Notes

Acknowledgements

The authors are very indebted to an anonymous referee for his/her careful reading and suggestions which helped to improve the readability of the paper.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia
  2. 2.Department Algebra GeometryPalacký UniversityOlomoucCzech Republic
  3. 3.Department of MathematicsUniversity of ColoradoBoulderUSA

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