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Banaschewski’s theorem for generalized MV-algebras

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Abstract

A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element.

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References

  1. B. Banaschewski: On lattice-ordered groups. Fund. Math. 55 (1964), 113–122.

    MATH  MathSciNet  Google Scholar 

  2. G. Birkhoff: Lattice Theory. Third Edition, Providence, 1967.

  3. P. Conrad: Lattice Ordered Groups. Tulane University, 1970.

  4. A. Dvurečenskij,: Pseudo MV-algebras are intervals of ℓ-groups. J. Austral. Math. Soc. 72 (2002), 427–445.

    Article  MATH  Google Scholar 

  5. A. Dvurečenskij, S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht, 2000.

    MATH  Google Scholar 

  6. G. Georgescu, A. Iorgulescu: Pseudo MV-algebras: a noncommutative extension of MV-algebras. In: The Proceedings of the Fourth International Symposium on Economic Informatics, INFOREC, Bucharest, 6–9 May, Romania. 1999, pp. 961–968.

  7. G. Georgescu, A. Iorgulescu: Pseudo MV-algebras. Multiple-Valued Logic 6 (2001), 95–135.

    MATH  MathSciNet  Google Scholar 

  8. J. Jakubík: Normal prime filters of a lattice ordered group. Czech. Math. J. 24 (1974), 91–96.

    Google Scholar 

  9. J. Jakubík: Subdirect product decompositions of MV-algebras. Czech. Math. J. 49 (1999), 163–173.

    Article  MATH  Google Scholar 

  10. J. Rachůnek: A non-commutative generalization of MV-algebras. Czech. Math. J. 52 (2002), 255–273.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Matematický ústav SAV, Grešákova 6, 040 01, Košice, Slovakia

    Ján Jakubík

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  1. Ján Jakubík
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Correspondence to Ján Jakubík.

Additional information

This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002.

The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information (grant I/2/2005).

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Jakubík, J. Banaschewski’s theorem for generalized MV-algebras. Czech Math J 57, 1099–1105 (2007). https://doi.org/10.1007/s10587-007-0115-z

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  • DOI: https://doi.org/10.1007/s10587-007-0115-z

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