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Lobachevskii Journal of Mathematics

, Volume 38, Issue 3, pp 420–428 | Cite as

Semigroups of centered upfamilies on groups

  • V. Gavrylkiv
Article

Abstract

Given a group G we study right and left zeros, idempotents, the minimal ideal, left cancellable and right cancellable elements of the semigroup N (G) of centered upfamilies and characterize groups G whose extensions N (G) are commutative. We finish the paper with the complete description of the structure of the semigroups N (G) for all groups G of cardinality |G| ≤ 4.

Keywords and phrases

Semigroup centered upfamily idempotent zero minimal ideal commutative 

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References

  1. 1.
    T. Banakh and V. Gavrylkiv, “Algebra in superextension of groups, II: cancelativity and centers,” Algebra DiscreteMath., No. 4, 1–14 (2008).MathSciNetzbMATHGoogle Scholar
  2. 2.
    T. Banakh and V. Gavrylkiv, “Algebra in superextension of groups: minimal left ideals,” Mat. Stud. 31, 142–148 (2009).MathSciNetzbMATHGoogle Scholar
  3. 3.
    T. Banakh and V. Gavrylkiv, “Algebra in the superextensions of twinic groups,” Dissertationes Math. 473, 74 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    T. Banakh and V. Gavrylkiv, “Algebra in superextensions of semilattices,” Algebra Discrete Math. 13 (1), 26–42 (2012).MathSciNetzbMATHGoogle Scholar
  5. 5.
    T. Banakh and V. Gavrylkiv, “Algebra in superextensions of inverse semigroups,” Algebra DiscreteMath. 13 (2), 147–168 (2012).MathSciNetzbMATHGoogle Scholar
  6. 6.
    T. Banakh and V. Gavrylkiv, “Characterizing semigroups whose superextensions are commutative,” Algebra Discrete Math. 17 (2), 161–192 (2014).MathSciNetzbMATHGoogle Scholar
  7. 7.
    T. Banakh and V. Gavrylkiv, “On structure of the semigroups of k-linked upfamilies on groups,” Asian-European J. Math. 10 (4), 15 (2017).Google Scholar
  8. 8.
    T. Banakh, V. Gavrylkiv, and O. Nykyforchyn, “Algebra in superextensions of groups, I: zeros and commutativity,” Algebra DiscreteMath., No. 3, 1–29 (2008).MathSciNetzbMATHGoogle Scholar
  9. 9.
    A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. 1: Mathematical Surveys (AMS, Providence, RI, 1961), Vol.7.Google Scholar
  10. 10.
    R. Dedekind, “Über Zerlegungen von Zahlen durch ihre grüssten gemeinsammen Teiler,” Gesammelte Werke 1, 103–148 (1897).Google Scholar
  11. 11.
    V. Gavrylkiv, “The spaces of inclusion hyperspaces over noncompact spaces,” Mat. Stud. 28, 92–110 (2007).MathSciNetzbMATHGoogle Scholar
  12. 12.
    V. Gavrylkiv, “Right-topological semigroup operations on inclusion hyperspaces,” Mat. Stud. 29, 18–34 (2008).MathSciNetzbMATHGoogle Scholar
  13. 13.
    V. Gavrylkiv, “Monotone families on cyclic semigroups,” Precarpathian Bull. Shevchenko Sci. Soc. 17 (1), 35–45 (2012).MathSciNetGoogle Scholar
  14. 14.
    V. Gavrylkiv, “Superextensions of cyclic semigroups,” Carpath. Math. Publ. 5 (1), 36–43 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    V. Gavrylkiv, “Semigroups of linked upfamilies,” Precarpathian Bull. Shevchenko Sci. Soc. 29 (1), 104–112 (2015).MathSciNetGoogle Scholar
  16. 16.
    N. Hindman and D. Strauss, Algebra in the Stone-Cech Compactification (de Gruyter, Berlin, New York, 1998).CrossRefzbMATHGoogle Scholar
  17. 17.
    J. van Mill, Supercompactness and Wallman Spaces, Vol. 85 of Math. Centre Tracts (Math. Centrum, Amsterdam, 1977).zbMATHGoogle Scholar
  18. 18.
    A. Teleiko and M. Zarichnyi, Categorical Topology of Compact Hausdofff Spaces (VNTL, Lviv, 1999).zbMATHGoogle Scholar
  19. 19.
    A. Verbeek, Superextensions of Topological Spaces, Vol. 41 of Math. Centre Tracts (Math. Centrum, Amsterdam, 1972).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Vasyl Stefanyk Precarpathian National UniversityIvano-FrankivskUkraine

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