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Atomic Effect Algebras with the Riesz Decomposition Property

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Abstract

We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any σ-orthocomplete atomic effect algebra with the Riesz Decomposition Property is an MV-effect algebras, and we apply this result for pseudo-effect algebras and for states.

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Acknowledgements

A.D. thanks for the support by Center of Excellence SAS—Quantum Technologies—, ERDF OP R&D Project meta-QUTE ITMS 26240120022, the grant VEGA No. 2/0059/12 SAV and by CZ.1.07/2.3.00/20.0051.

Y.X. thanks for the support by SAIA, n.o. (Slovak Academic Information Agency) and the Ministry of Education, Science, Research and Sport of the Slovak Republic. This work is also supported by National Science Foundation of China (Grant No. 60873119), and the Fundamental Research Funds for the Central Universities (Grant No. GK200902047).

The authors are very indebted to an anonymous referee for his careful reading and suggestions which helped us to improve the readability of the paper.

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Authors and Affiliations

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

    Anatolij Dvurečenskij & Yongjian Xie

  2. Depar. Algebra Geom., Palacký Univer., 771 46, Olomouc, Czech Republic

    Anatolij Dvurečenskij

  3. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Yongjian Xie

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  1. Anatolij Dvurečenskij
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  2. Yongjian Xie
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Correspondence to Yongjian Xie.

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Dvurečenskij, A., Xie, Y. Atomic Effect Algebras with the Riesz Decomposition Property. Found Phys 42, 1078–1093 (2012). https://doi.org/10.1007/s10701-012-9655-7

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  • DOI: https://doi.org/10.1007/s10701-012-9655-7

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