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Combining boolean algebras and ℓ-groups in the variety generated by chang’s mv-algebra

  • A. Di Nola EMAIL logo , A. R. Ferraioli and B. Gerla
Published/Copyright: July 4, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 2

Abstract

In this paper we investigate a class of MV-algebras built up by fixing a Boolean algebra, one of its maximal ideals and an ℓ-group. We use such class to characterize, in the variety generated by all perfect MV-algebras, those MV-algebras which have their perfect skeleton as a quotient, giving an axiomatization of such a class and a representation theorem.

MSC 2010: Primary 06D35; Secondary 06F20
Keywords: MV-algebras; perfect MV-algebras; lattice-ordered abelian groups

Dedicated to Professor Anatolij Dvurečenskij on the occasion of his 65th birthday

(Communicated by Sylvia Pulmannová)

REFERENCES

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Received: 2014-2-12
Accepted: 2014-9-22
Published Online: 2016-7-4
Published in Print: 2016-4-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0144
Keywords for this article
MV-algebras; perfect MV-algebras; lattice-ordered abelian groups

Articles in the same Issue

  1. Research Article
  2. Holistic logical arguments in quantum computation
  3. Research Article
  4. States with values in the Łukasiewicz groupoid
  5. Research Article
  6. On realization of effect algebras
  7. Research Article
  8. States on symmetric logics: extensions
  9. Research Article
  10. Extensions and measurability in quantum measure spaces
  11. Research Article
  12. Convex subalgebras of upper bounded GMV-algebras
  13. Research Article
  14. Combining boolean algebras and ℓ-groups in the variety generated by chang’s mv-algebra
  15. Research Article
  16. Large rigid sets of algebras with respect to embeddability
  17. Research Article
  18. Conformal algebras, vertex algebras, and the logic of locality
  19. Research Article
  20. Extension of measures on pseudo-D-lattices
  21. Research Article
  22. Note on a parameter switching method for nonlinear ODEs
  23. Research Article
  24. Compatibility for probabilistic theories
  25. Research Article
  26. Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras
  27. Research Article
  28. Commutativity in a synaptic algebra
  29. Research Article
  30. Discrete averaged mixing applied to the logarithmic distributions
  31. Research Article
  32. Automorphisms of decompositions
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