On the semigroup of non-injective monoid endomorphisms of the semigroup Bωℱ  with the two-element family ℱ of inductive nonempty subsets of ω

Oleg Gutik, Inna Pozdniakova

Анотація


We study the semigroup of non-injective monoid endomorphisms of the semigroup Bωℱ  with the two-elements family ℱ  of inductive nonempty subsets of ω. We describe the structure of elements of the semigroup End0*(Bωℱ) of non-injective monoid endomorphisms of the semigroup BωF. In particular we show that its subsemigroup End*(Bωℱ) of  non-injective non-annihilating  monoid endomorphisms of the semigroup Bωℱ is isomorphic to the direct product of the two-element left-zero semigroup and the multiplicative semigroup of positive integers and describe Green's relations on End*(Bωℱ).

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A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, Vol. I., Amer. Math. Soc. Surveys 7, Providence, R.I., 1961.

A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, Vol. II., Amer. Math. Soc. Surveys 7, Providence, R.I., 1967.

O. Gutik and O. Lysetska, On the semigroup Bωℱ which is generated by the family ℱ of atomic subsets of ω, Visn. L'viv. Univ., Ser. Mekh.-Mat. 92 (2021) 34-50. DOI: 10.30970/vmm.2021.92.034-050

O. Gutik and M. Mykhalenych, On some generalization of the bicyclic monoid, Visnyk Lviv. Univ. Ser. Mech.-Mat. 90 (2020), 5-19 (in Ukrainian). DOI: 10.30970/vmm.2020.90.005-019

O. Gutik and M. Mykhalenych, On group congruences on the semigroup Bωℱ and its homomorphic retracts in the case when the family ℱ consists of inductive non-empty subsets of ω, Visnyk Lviv. Univ. Ser. Mech.-Mat. 91 (2021), 5-27 (in Ukrainian). DOI: 10.30970/vmm.2021.91.005-027

O. Gutik and M. Mykhalenych, On automorphisms of the semigroup Bωℱ in the case when the family ℱ consists of nonempty inductive subsets of ω, Visnyk Lviv. Univ. Ser. Mech.-Mat. 93 (2022), 54-65. (in Ukrainian). DOI: 10.30970/vmm.2022.93.054-065

O. Gutik and I. Pozdniakova, On the semigroup of injective monoid endomorphisms of the monoid Bωℱ with the two-elements family ℱ of inductive nonempty subsets of ω, Visnyk L'viv. Univ. Ser. Mech.-Mat. 94 (2022), 32-55. DOI: 10.30970/vmm.2022.94.032-055

O. Gutik, O. Prokhorenkova, and D. Sekh, On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup, Visn. L'viv. Univ., Ser. Mekh.-Mat. 92 (2021) 5-16 (in Ukrainian). DOI: 10.30970/vmm.2022.93.042-053

M. Lawson, Inverse semigroups. The theory of partial symmetries, World Scientific, Singapore, 1998.

O. Lysetska, On feebly compact topologies on the semigroup Bωℱ1, Visnyk Lviv. Univ. Ser. Mech.-Mat. 90 (2020), 48-56. DOI: 10.30970/vmm.2020.90.048-056

M. Petrich, Inverse semigroups, John Wiley & Sons, New York, 1984.

V. V. Wagner, Generalized groups, Dokl. Akad. Nauk SSSR 84 (1952), 1119-1122 (in Russian).




DOI: http://dx.doi.org/10.30970/vmm.2023.95.014-027

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