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Product Effect Algebras

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Abstract

We introduce a product on an effect algebra. We prove that every product effect algebra with the Riesz decomposition property (RDP), is an interval in an Abelian unital interpolation po-ring, and we show that the category of product effect algebras with the RDP is categorically equivalent with the category of unital Abelian interpolation po-rings. In addition, we show that every product effect algebra with the RDP and with 1 as a product unity is a subdirect product of antilattice product effect algebras with the RDP.

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REFERENCES

  • Chang, C. C. (1958). Algebraic analysis of many valued logics. Transactions of American Mathematical Society 88, 467–490.

    Google Scholar 

  • Di Nola, A. and Dvurečenskij, A. (2001). Product MV-algebras. Multi. Val. Logic 6, 193–215.

    Google Scholar 

  • Dvurečenskij, A. Perfect effect algebras are categorically equivalent with Abelian interpolation pogroups.

  • Dvurečenskij, A. and Pulmannová, S. (2000). New Trends in Quantum Structures, Kluwer, Dordrecht.

    Google Scholar 

  • Dvurečenskij, A. and Rieč?an, B. (1999).Weakly divisible MV-algebras and product, Journal of Mathematical Analysis and Applications 234, 208–222.

    Google Scholar 

  • Foulis, D. J. and Bennett, M. K. (1994). Effect algebras and unsharp quantum logics, Foundations of Physics 24, 1325–1346.

    Google Scholar 

  • Goodearl, K. R. (1986). Partially Ordered Abelian Groups with Interpolation, Mathematical Surveys and Monographs No. 20, American Mathematical Society, Providence, Rhode Island.

    Google Scholar 

  • Kôpka, F. and Chovanec, F. (1994). D-posets, Math. Slovaca 44, 21–34.

    Google Scholar 

  • MacLane, S. (1971). Categories for the Working Mathematician, Springer, New York.

    Google Scholar 

  • Ravindran, K. (1996). On a Structure Theory of Effect Algebras, Ph. D. Thesis, Kansas State University, Manhattan, Kansas.

    Google Scholar 

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Authors and Affiliations

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

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Dvurečenskij, A. Product Effect Algebras. International Journal of Theoretical Physics 41, 1827–1839 (2002). https://doi.org/10.1023/A:1021017905403

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  • DOI: https://doi.org/10.1023/A:1021017905403

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