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Hull determination and type decomposition for a generalized effect algebra

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Abstract

In this article, we show that certain generalized boolean subalgebras of the exocenter of a generalized effect algebra (GEA) determine hull systems on the GEA in a manner analogous to the determination of a hull mapping on an effect algebra (EA) by its set of invariant elements. We show that a hull system on a GEA E induces a hull mapping on each interval E[0, p] in E, and, using hull systems, we identify certain special elements of E (e.g., η-subcentral elements, η-monads, and η-dyads). We also extend the type-decomposition theory for EAs to GEAs.

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Correspondence to David J. Foulis.

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Presented by F. Wehrung.

The second author was supported by ERDF OP R&D metaQUTE ITMS 26240120022 and grant VEGA 2/0059/12, and by the Slovak Research and Development Agency under the contract APVV- 0178-11.

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Foulis, D.J., Pulmannová, S. Hull determination and type decomposition for a generalized effect algebra. Algebra Univers. 69, 45–81 (2013). https://doi.org/10.1007/s00012-012-0214-z

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  • DOI: https://doi.org/10.1007/s00012-012-0214-z

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