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A note on residuated po-groupoids and lattices with antitone involutions

  • Ivan Chajda EMAIL logo and Jan Kühr
Published/Copyright: June 7, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 3

Abstract

Following [BOTUR, M.—CHAJDA, I.—HALAŠ, R.: Are basic algebras residuated structures?, Soft Comput. 14 (2010), 251—255] we discuss the connections between left-residuated partially ordered groupoids and the so-called basic algebras, which are a non-commutative and non-associative generalization of MV-algebras and orthomodular lattices.

MSC 2010: Primary 03G10; 03G25
Keywords: basic algebra; lattice with antitone involutions; left-residuated po-groupoid

Supported by the bilateral project “New perspectives on residuated posets” of the Austrian Science Fund (FWF): project I 1923-N25, and the Czech Science Foundation (GAČR): project 15-34697L. Partially supported by the projects “Mathematical structures” of the Palacký University: projects IGA PrF 2014016 and IGA PrF 2015010.

(Communicated by Jiří Rachůnek)

References

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Received: 2014-9-3
Accepted: 2015-10-1
Published Online: 2017-6-7
Published in Print: 2017-6-27

© 2017 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  2. Some results in local Hilbert algebras
  4. A note on residuated po-groupoids and lattices with antitone involutions
  6. The first law of cubology for the Rubik’s Revenge
  8. Conditional associativity in orthomodular lattices
  10. A monotonicity property for generalized Fibonacci sequences
  12. Systems of conditionally independent sets
  14. On the k-th order lfsr sequence with public key cryptosystems
  16. On parametric spaces of bicentric quadrilaterals
  18. Character sums with an explicit evaluation
  20. Some remarks on formal power series and formal Laurent series
  22. The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
  24. On prime and semiprime generalized hyperaction of hypermonoid
  26. On O’Malley ϱ-upper continuous functions
  28. Uniqueness theorems for finitely additive probabilities on quantum structures
  30. Some results on differential-difference analogues of Brück conjecture
  32. Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
  34. On support, separation and decomposition theorems for t-Wright-concave functions
  36. A characterization of holomorphic bivariate functions of bounded index
  38. Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
  40. The geometry of two-valued subsets of Lp-spaces
  42. Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
  44. A comparison of two tests in multivariate models
  46. Modelling prescription behaviour of general practitioners
  48. Characterization of congruence lattices of principal p-algebras
https://doi.org/10.1515/ms-2016-0289
Keywords for this article
basic algebra; lattice with antitone involutions; left-residuated po-groupoid

Articles in the same Issue

  2. Some results in local Hilbert algebras
  4. A note on residuated po-groupoids and lattices with antitone involutions
  6. The first law of cubology for the Rubik’s Revenge
  8. Conditional associativity in orthomodular lattices
  10. A monotonicity property for generalized Fibonacci sequences
  12. Systems of conditionally independent sets
  14. On the k-th order lfsr sequence with public key cryptosystems
  16. On parametric spaces of bicentric quadrilaterals
  18. Character sums with an explicit evaluation
  20. Some remarks on formal power series and formal Laurent series
  22. The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
  24. On prime and semiprime generalized hyperaction of hypermonoid
  26. On O’Malley ϱ-upper continuous functions
  28. Uniqueness theorems for finitely additive probabilities on quantum structures
  30. Some results on differential-difference analogues of Brück conjecture
  32. Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
  34. On support, separation and decomposition theorems for t-Wright-concave functions
  36. A characterization of holomorphic bivariate functions of bounded index
  38. Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
  40. The geometry of two-valued subsets of Lp-spaces
  42. Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
  44. A comparison of two tests in multivariate models
  46. Modelling prescription behaviour of general practitioners
  48. Characterization of congruence lattices of principal p-algebras
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