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, Volume 32, Issue 2, pp 189–204 | Cite as

Unitizing a Generalized Pseudo Effect Algebra

  • David J. Foulis
  • Sylvia Pulmannová
Article

Abstract

As is well-known, every generalized effect algebra can be embedded as a maximal proper ideal in an effect algebra called its unitization. We show that a necessary and sufficient condition that a generalized pseudo effect algebra can similarly be embedded as a maximal proper ideal in a pseudo effect algebra is that it admits a so-called unitizing automorphism. On the other hand, we show that a pseudo effect algebra is a unitization of a generalized pseudo effect algebra if and only if it admits a two-valued state.

Keywords

Pseudo effect algebra Generalized pseudo effect algebra Unitization Unitizing automorphism Two-valued state 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  2. 2.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia

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