References

  1. Banakh T., Gavrylkiv V. Algebra in superextension of groups, II: cancelativity and centers. Algebra Discrete Math. 2008, 7 (4), 1–14.
  2. Banakh T., Gavrylkiv V. Algebra in superextension of groups: minimal left ideals. Mat. Stud. 2009, 31 (2), 142–148. doi:10.30970/ms.31.2.142-148
  3. Banakh T., Gavrylkiv V. Extending binary operations to functor-spaces. Carpathian Math. Publ. 2009, 1 (2), 113–126.
  4. Banakh T., Gavrylkiv V. Algebra in superextensions of semilattices. Algebra Discrete Math. 2012, 13 (1), 26–42.
  5. Banakh T., Gavrylkiv V. Characterizing semigroups with commutative superextensions. Algebra Discrete Math. 2014, 17 (2), 161–192.
  6. Banakh T., Gavrylkiv V. On structure of the semigroups of k-linked upfamilies on groups. Asian-European J. Math. 2017, 10 (4), 1750083. doi:10.1142/S1793557117500838.
  7. Banakh T., Gavrylkiv V. Automorphism groups of superextensions of groups. Mat. Stud. 2017, 48 (2), 134–142. doi:10.15330/ms.48.2.134-142
  8. Banakh T., Gavrylkiv V., Nykyforchyn O. Algebra in superextension of groups, I: zeros and commutativity. Algebra Discrete Math. 2008, 7 (3), 1–29.
  9. Boyd S.J., Gould M., Nelson A. Interassociativity of Semigroups. In: Proceedings of the Tennessee Topology Conference. World Scientific, 1997, 33–51.
  10. Brouwer A.E., Mills C.F., Mills W.H., Verbeek A. Counting families of mutually intesecting sets. Electron. J. Combin. 2013, 20 (2), 8.
  11. Drouzy M. La structuration des ensembles de semigroupes d’ordre 2, 3 et 4 par la relation d’interassociativité. Manuscript 1986.
  12. Gavrylkiv V. The spaces of inclusion hyperspaces over noncompact spaces. Mat. Stud. 2007, 28 (1), 92–110.
  13. Gavrylkiv V. Right-topological semigroup operations on inclusion hyperspaces. Mat. Stud. 2008, 29 (1), 18–34.
  14. Gavrylkiv V. Semigroups of centered upfamilies on groups. Lobachevskii J. Math. 2017, 38 (3), 420–428. doi:10.1134/S1995080217030106
  15. Gavrylkiv V. On the automorphism group of the superextension of a semigroup. Mat. Stud. 2017, 48 (1), 3–13. doi:10.15330/ms.48.1.3-13
  16. Gavrylkiv V. Automorphisms of semigroups of \(k\)-linked upfamilies. J. Math. Sci. 2018, 234 (1), 21–34. doi:10.1007/s10958-018-3978-7
  17. Gavrylkiv V. Automorphism groups of semigroups of upfamilies. Asian-European J. Math. 2020, 13 (1), 2050099. doi:10.1142/S1793557120500990
  18. Gavrylkiv V.M., Rendziak D.V. Interassociativity and three-element doppelsemigroups. Algebra Discrete Math. 2019, 28 (2), 224–247.
  19. Gavrylkiv V.M. Doppelsemigroups of \(k\)-linked upfamilies. J. Algebra Appl. 2026, 25, article 2650207. doi:10.1142/S0219498826502075
  20. Gavrylkiv V.M. Note on cyclic doppelsemigroups. Algebra Discrete Math. 2022, 34 (1), 15–21.
  21. Gavrylkiv V.M. Note on the number of doppelsemigroups of small order. Res. Math. (to appear)
  22. Gavrylkiv V.M. On the upfamily extension of a doppelsemigroup. Mat. Stud. 2024, 61 (2), 123–135. doi:10.30970/ms.61.2.123-135
  23. Gould M., Richardson R.E. Translational hulls of polynomially related semigroups. Czechoslovak Math. J. 1983, 33 (1), 95–100. doi:10.21136/CMJ.1983.101858
  24. Hickey J.B. Semigroups under a sandwich operation. Proc. Edinburgh Math. Soc. 1983, 26 (3), 371–382. doi:10.1017/S0013091500004442
  25. Hindman N., Strauss D. Algebra in the Stone-Čech compactification. de Gruyter, Berlin, 1998.
  26. Loday J.L. Dialgebras. In: Dialgebras and related operads. Lect. Notes Math. 1763. Springer-Verlag, Berlin, 2001, 7–66.
  27. van Mill J. Supercompactness and Wallman spaces. Mathematical Centre, Amsterdam, 1977.
  28. Pirashvili T. Sets with two associative operations. Cent. Eur. J. Math. 2003, 1 (2), 169–183. doi:10.2478/BF02476006
  29. Richter B. Dialgebren, Doppelalgebren und ihre Homologie. Diplomarbeit, Universitat Bonn, Bonn, 1997.
  30. Schein B.M. Restrictive semigroups and bisemigroups. Technical Report. University of Arkansas, Fayetteville, 1989.
  31. Schein B.M. Restrictive bisemigroups. Izv. Vyssh. Uchebn. Zaved. Mat. 1965, 1 (44), 168–179. (in Russian)
  32. Verbeek A. Superextensions of topological spaces. Mathematical Centre, Amsterdam, 1972.
  33. Zhuchok A.V., Demko M. Free \(n\)-dinilpotent doppelsemigroups. Algebra Discrete Math. 2016, 22 (2), 304–316.
  34. Zhuchok A.V. Free products of doppelsemigroups. Algebra Univers. 2017, 77 (3), 361–374. doi:10.1007/s00012-017-0431-6
  35. Zhuchok A.V. Free left \(n\)-dinilpotent doppelsemigroups. Commun. Algebra. 2017, 45 (11), 4960–4970. doi:10.1080/00927872.2017.1287274
  36. Zhuchok A.V. Structure of free strong doppelsemigroups. Commun. Algebra. 2018, 46 (8), 3262–3279. doi:10.1080/00927872.2017.1407422
  37. Zhuchok A.V., Knauer K. Abelian doppelsemigroups. Algebra Discrete Math. 2018, 26 (2), 290–304.
  38. Zhuchok A.V. Relatively free doppelsemigroups. Monograph series Lectures in Pure and Applied Mathematics, 5. Potsdam University Press, Potsdam, 2018.
  39. Zhuchok A.V., Zhuchok Yul. V., Koppitz J. Free rectangular doppelsemigroups. J. Algebra Appl. 2020, 19 (11), 2050205. doi:10.1142/S0219498820502059
  40. Zhuchok Yu.V., Koppitz J. Representations of ordered doppelsemigroups by binary relations. Algebra Discrete Math. 2019, 27 (1), 144–154.