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Dimension theory for generalized effect algebras

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Abstract

In this paper, we define and study dimension generalized effect algebras (DGEAs), i.e., Dedekind orthocomplete and centrally orthocomplete generalized effect algebras equipped with a dimension equivalence relation. Our theory is a bona fide generalization of the theory of dimension effect algebras (DEAs), i.e., it is formulated so that if a DGEA happens to be an effect algebra (i.e., it has a unit element), then it is a DEA. We prove that a DGEA decomposes into type I, II, and III DGEAS in a manner analogous to the type I/II/III decomposition of a DEA.

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Author notes

  1. David J. Foulis

    Present address: , 1 Sutton Court, Amherst, MA, 01002, USA

Authors and Affiliations

  1. Emeritus Professor of Mathematics, Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    David J. Foulis

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

    Sylvia Pulmannová

Authors
  1. David J. Foulis
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  2. Sylvia Pulmannová
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Corresponding author

Correspondence to Sylvia Pulmannová.

Additional information

Presented by F. Wehrung.

The second author was supported by the Center of Excellence SAS – Quantum Technologies; ERDF OP R&D Project meta-QUTE ITMS 26240120022; the grant VEGA No. 2/0059/12 SAV; and the Slovak Research and Development Agency under the contract APVV-0178-11.

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Foulis, D.J., Pulmannová, S. Dimension theory for generalized effect algebras. Algebra Univers. 69, 357–386 (2013). https://doi.org/10.1007/s00012-013-0237-0

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  • DOI: https://doi.org/10.1007/s00012-013-0237-0

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