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Lexico groups and direct products of lattice ordered groups

  • Ján Jakubík EMAIL logo
Published/Copyright: April 26, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

A lattice ordered group A will be said to be a lexico group if there exists a convex ℓ-subgroup A0 of A with A0 ≠ A such that for each a ∈ A\A0 we have either a > a0 for each a0 ∈ A0, or a < a0 for each a0 ∈ A0. We prove the following result. Let A be a convex ℓ-subgroup of a lattice ordered group ∈ such that

  1. A is a lexico group, and

  2. A fails to be upper bounded in G.

Then A is a direct factor of G.

Keywords: lattice ordered group; lexico group; directed product
MSC: Primary 01A70; 06D35

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

  1. This paper has been communicated by Jiří Rachůnek.

References

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Received: 2012-10-17
Accepted: 2013-4-22
Published Online: 2016-4-26
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0113
Keywords for this article
lattice ordered group; lexico group; directed product

Articles in the same Issue

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
  32. Inclusion properties for classes of analytic functions associated with conic domains
  33. Research Article
  34. Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial
  35. Research Article
  36. Solutions and constrained null-controllability for a differential-difference equation
  37. Research Article
  38. Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
  39. Research Article
  40. Time periodic solutions for a sixth order nonlinear parabolic equation
  41. Research Article
  42. Some inequalities of trigonometric approximation in weighted Orlicz spaces
  43. Research Article
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  45. Research Article
  46. Dichotomies for Orlicz spaces
  47. Research Article
  48. On freely generated semigraph C*-algebras
  49. Research Article
  50. Operators with a given part of the numerical range
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  53. Research Paper
  54. Confidence regions in singular weakly nonlinear regression models with constraints
  55. Research Article
  56. Global stability of an SEI model for plant diseases
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