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Associativity and Distributivity-Like Properties in Generalized Effect Algebras

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Abstract

We prove “large” associativity of the partial plus operation in generalized effect algebras and present an overview of distributivity-like properties of partial operations plus and minus in generalized effect algebras with respect to (possibly infinite) suprema and infima and vice versa. These results generalize previous results in various subclasses of generalized effect algebras.

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References

  1. Foulis, D.J.; Randall, C.H.: Empirical Logic and Tensor Products. In Interpretations and Foundations of Quantum Theory (Grundlagen der exakten Naturwissenschaften, Bd. 5), Mannheim (1981)

  2. Giuntini, R., Greuling, H.: Toward a formal language for unsharp properties. Found. Phys. 19, 931–945 (1989). https://doi.org/10.1007/BF01889307

    Article  MathSciNet  ADS  Google Scholar 

  3. Foulis, D.J., Bennett, M.K.: Effect algebras and unsharp quantum logics. Found. Phys. 24, 1331–1352 (1994). https://doi.org/10.1007/BF02283036

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  5. Dvurečenskij, A., Pulmannová, S.: Tensor product of D-posets and D-test spaces. Rep. Math. Phys. 34, 251–275 (1994). https://doi.org/10.1016/0034-4877(94)90001-9

    Article  MathSciNet  MATH  ADS  Google Scholar 

  6. Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Academic Publishers, Bratislava (2000). https://doi.org/10.1007/BF00676241

  7. Riečanová, Z.: On order continuity of quantum structures and their homomorphisms. Demonstr. Math. 29, 433–443 (1996). https://doi.org/10.1515/dema-1996-0220

    Article  MathSciNet  MATH  Google Scholar 

  8. Ji, W.: Characterization of homogeneity in orthocomplete atomic effect algebras. Fuzzy Sets Syst. 236, 113–121 (2014). https://doi.org/10.1016/j.fss.2013.06.005

    Article  MathSciNet  MATH  Google Scholar 

  9. Tkadlec, J.: Distributivity and associativity in effect algebras. Fuzzy Sets Syst. 289, 151–156 (2016). https://doi.org/10.1016/j.fss.2015.06.025

    Article  MathSciNet  MATH  Google Scholar 

  10. Bennett, M., Foulis, D.: Phi-symmetric effect algebras. Found. Phys. 25, 1699–1722 (1995). https://doi.org/10.1007/BF02057883

    Article  MathSciNet  ADS  Google Scholar 

  11. Chovanec, F., Kôpka, F.: D-lattices. Internat. J. Theoret. Phys. 34, 1297–1302 (1995). https://doi.org/10.1007/BF00676241

    Article  MathSciNet  MATH  ADS  Google Scholar 

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Funding

This work was supported by the project OPVVV CAAS CZ.02.1.01/0.0/0.0/16_019/0000778 of the Ministry of Education, Youth and Sports of the Czech Republic and by the Grant Agency of the Czech Technical University in Prague, grant No. SGS16/074/OHK3/1T/13.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, 166 27, Praha, Czech Republic

    Josef Tkadlec & Petr Žáček

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  1. Josef Tkadlec
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  2. Petr Žáček
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All authors contributed to the paper equally. All authors read and approved the final manuscript.

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Correspondence to Josef Tkadlec.

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Tkadlec, J., Žáček, P. Associativity and Distributivity-Like Properties in Generalized Effect Algebras. Int J Theor Phys 62, 117 (2023). https://doi.org/10.1007/s10773-023-05371-3

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