International Journal of Theoretical Physics

, Volume 54, Issue 12, pp 4260–4271 | Cite as

Quantum Structures Versus Partially Ordered Groups

  • Anatolij Dvurečenskij


We present a survey of applications of partially ordered groups (= po-groups) in quantum structures. The survey has two levels: (1) To show when an effect algebra or a pseudo effect algebra is an interval in the positive cone of a po-group. A sufficient condition is a kind of the Riesz Decomposition Property, i.e. a property when two decompositions have a joint refinement. (2) Using an arbitrary power of the positive and negative cone of a po-group and two injections, we can construct a large class of pseudo effect algebras which are called kite pseudo effect algebras, and we describe basic properties of this class.


Effect algebra Pseudo effect algebra Pseudo MV-algebra -group Po-group Strong unit Riesz decomposition property Kite pseudo effect algebra Subdirectly irreducible kite 



The author is 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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© Springer Science+Business Media New York 2014

Authors and Affiliations

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

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