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Unitizations of Generalized Pseudo Effect Algebras and their Ideals

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Abstract

A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphism, paying special attention to the behavior of congruences, ideals, and the Riesz decomposition property in this setting.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, 1 Sutton Court, Amherst, MA, 01002, USA

    David J. Foulis

  2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Sylvia Pulmannová & Elena Vinceková

Authors
  1. David J. Foulis
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  2. Sylvia Pulmannová
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  3. Elena Vinceková
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Corresponding author

Correspondence to David J. Foulis.

Additional information

The second and third authors were supported by Research and Development Support Agency under the contract No. APVV-0178-11 and grant VEGA 2/0059/12.

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Foulis, D.J., Pulmannová, S. & Vinceková, E. Unitizations of Generalized Pseudo Effect Algebras and their Ideals. Order 33, 311–332 (2016). https://doi.org/10.1007/s11083-015-9368-6

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  • DOI: https://doi.org/10.1007/s11083-015-9368-6

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