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Convex subalgebras of upper bounded GMV-algebras

  • Ján Jakubík EMAIL logo
Published/Copyright: July 31, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 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

[1] Dvurečenskij, A.: Pseudo MV-algebras are intervals in ℓ-groups, J. Aust. Math. Soc. 72 (2004), 427–445.10.1017/S1446788700036806Search in Google Scholar

[2] Dvurečenskij, A.: States on pseudo MV-algebras, Studia Logica 68 (2001), 301–327.10.1023/A:1012490620450Search in Google Scholar

[3] Galatos, N.—Tsinakis, C.: Generalized MV-algebras, J. Algebra 283(2005), 254–291.10.1016/j.jalgebra.2004.07.002Search in Google Scholar

[4] Georgescu, G.—Iorgulescu, A.: Pseudo MV-algebras: a noncommutative extension of MV-algebras. In: Information Technology, Bucharest 1999, INFOREC, Bucharest, 1999, pp. 961–968.Search in Google Scholar

[5] Georgescu, G.—Iorgulescu, A.: Pseudo MV-algebras, Mult.-Valued Logic 6 (2001), 95–135.Search in Google Scholar

[6] Glass, A. M. W.: Partially Ordered Groups, World Scientific, Singapore-New Jersey-London-Hong Kong, 1999.10.1142/3811Search in Google Scholar

[7] JakubíK, J.: Radical classes and weak retract mappings of generalized MV-algebras, Math. Slovaca 58 (2008), 719–738.10.2478/s12175-008-0104-1Search in Google Scholar

[8] Rachŭnek, J.: A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255–273.10.1023/A:1021766309509Search in Google Scholar

[9] Rachŭnek, J.: Prime spectra of a non-commutative generalization of MV-algebras, Algebra Universalis 48 (2002), 151–169.10.1007/PL00012447Search in Google Scholar

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
Keywords for this article
lattice ordered group; convex ℓ-subgroup; ℓ-ideal; upper bounded GMV-algebra; convex subalgebra; ideal

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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