References

  1. Clifford A.H., Preston G.B. The algebraic theory of semigroups. Vol. I. Math. Surveys Monogr., 7. Providence, R.I., 1961.
  2. Clifford A.H., Preston G.B. The algebraic theory of semigroups. Vol. II. Math. Surveys Monogr., 7. Providence, R.I., 1967.
  3. Gutik O., Lysetska O. On the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}}\) which is generated by the family \(\mathscr{F}\) of atomic subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2021, 92, 34–50. doi:10.30970/vmm.2021.92.034-050
  4. Gutik O., Mykhalenych M. On some generalization of the bicyclic monoid. Visnyk Lviv Univ. Ser. Mech.-Mat. 2020, 90, 5–19. doi:10.30970/vmm.2020.90.005-019 (in Ukrainian)
  5. Gutik O., Mykhalenych M. On group congruences on the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}}\) and its homomorphic retracts in the case when the family \(\mathscr{F}\) consists of inductive non-empty subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2021, 91, 5–27. doi:10.30970/vmm.2021.91.005-027 (in Ukrainian)
  6. Gutik O., Mykhalenych M. On automorphisms of the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}}\) in the case of a family \(\mathscr{F}\) nonempty inductive subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2022, 93, 54–65. doi:10.30970/vmm.2022.93.054-065 (in Ukrainian)
  7. Gutik O.V., Popadiuk O.B. On the semigroup of injective endomorphisms of the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}_n}\) generated by the family \(\mathscr{F}_n\) of initial finite intervals in \(\omega\). J. Math. Sci. 2024, 282 (5), 646–667. doi:10.1007/s10958-024-07207-9 (translation of Mat. Metody Fiz.-Mekh. Polya 2022, 65 (1–2), 42–57. (in Ukrainian))
  8. Gutik O.V., Popadiuk O.B. On the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}_n}\), which is generated by the family \(\mathscr{F}_n\) of finite bounded intervals of \(\omega\). Carpathian Math. Publ. 2023, 15 (2), 331–355. doi:10.15330/cmp.15.2.331-355
  9. Gutik O., Pozdniakova I. On the semigroup of injective monoid endomorphisms of the monoid \(\boldsymbol{B}_{\omega}^{\mathscr{F}}\) with the two-elements family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2022, 94, 32–55. doi:10.30970/vmm.2022.94.032-055
  10. Gutik O., Pozdniakova I. On the semigroup of non-injective monoid endomorphisms of the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}}\) with the two-element family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2023, 95, 14–27. doi:10.30970/vmm.2023.95.014-027
  11. Gutik O., Pozdniakova I. On the group of automorphisms of the semigroup \(\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\). Algebra Discrete Math. 2023, 35 (1), 42–61. doi:10.12958/adm2010
  12. Gutik O., Pozdniakova I. On the semigroup of all monoid endomorphisms of the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}}\) with the two-elements family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2024, 96, 5–24. doi:10.30970/vmm.2024.96.005-024
  13. Gutik O., Prokhorenkova O., Sekh D. On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup. Visnyk Lviv Univ. Ser. Mech.-Mat. 2021, 92, 5–16. doi:10.30970/vmm.2021.92.005-016 (in Ukrainian)
  14. Gutik O., Serivka M. On the semigroup of injective monoid endomorphisms of the monoid \(\boldsymbol{B}_{\omega}^{\mathscr{F}^3}\) with a three element family \(\mathscr{F}^3\) of inductive nonempty subsets of \(\omega\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2023, 95, 28–45. doi:10.30970/vmm.2023.95.028-045
  15. Gutik O.V., Serivka M.V. On the semigroup of endomorphisms of the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}^2}\) with the two-element family \(\mathscr{F}^2\) of inductive nonempty subsets of \(\omega\). Nauk. Visn. Uzhgorod. Univ., Ser. Mat. Inform. 2025, 47 (2), 43–51. doi:10.24144/2616-7700.2025.47(2).43-51 (in Ukrainian)
  16. Lawson M. Inverse semigroups. The theory of partial symmetries. World Scientific, Singapore, 1998. doi:10.1142/3645
  17. Lysetska O. On feebly compact topologies on the semigroup \(\boldsymbol{B}_{\omega}^{\mathscr{F}_1}\). Visnyk Lviv Univ. Ser. Mech.-Mat. 2020, 90, 48–56. doi:10.30970/vmm.2020.90.048-056
  18. Petrich M. Inverse semigroups. John Wiley \(\&\) Sons, New York, 1984.
  19. Popadiuk O. On endomorphisms of the inverse semigroup of convex order isomorphisms of the set \(\omega\) of a bounded rank which are generated by Rees congruences. Visnyk Lviv Univ. Ser. Mech.-Mat. 2022, 93, 34–41. doi:10.30970/vmm.2022.93.034-041
  20. Wagner V.V. Generalized groups. Dokl. Akad. Nauk SSSR 1952, 84, 1119–1122 (in Russian).