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Convex subalgebras of upper bounded GMV-algebras

  • Ján Jakubík EMAIL logo
Veröffentlicht/Copyright: 31. Juli 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 2

Abstract

We apply the notion of generalized MV-algebra (GMV-algebra, for short) in the sense introduced and studied by Galatos and Tsinakis. Let M be an upper bounded GMV-algebra. Then M can be constructed by using a pair (G1, L), where G1 is a lattice ordered group and L is a filter on the lattice G1− satisfying certain conditions. In the present paper we deal with the relations between convex subalgebras of M and convex ℓ-subgroups of G1.

Keywords: lattice ordered group; convex ℓ-subgroup; ℓ-ideal; upper bounded GMV-algebra; convex subalgebra; ideal
MSC 2010: Primary 06D35

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

(Communicated by Sylvia Pulmannová)

The paper has been supported by Slovak Research and Development Agency under the contract APVV-0178-11.

References

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Received: 2014-2-12
Accepted: 2014-3-21
Published Online: 2016-7-31
Published in Print: 2016-4-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0143
Schlagwörter für diesen Artikel
lattice ordered group; convex ℓ-subgroup; ℓ-ideal; upper bounded GMV-algebra; convex subalgebra; ideal

Artikel in diesem Heft

  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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