On the semigroup of non-injective monoid endomorphisms of the semigroup B_ω^F with the two-element family F of inductive nonempty subsets of ω
Олег Гутік, Inna Pozdniakova · Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna · 2023
We study the semigroup of non-injective monoid endomorphisms of the semigroup B ω ℱ with the two-elements family ℱ of inductive nonempty subsets of ω. We describe the structure of elements of the semigroup End 0 * (B ω ℱ ) of non-injective monoid endomorphisms of the semigroup BωF. In particular we show that its subsemigroup End * (B ω ℱ ) of non-injective non-annihilating monoid endomorphisms of the semigroup B ω ℱ 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 * (B ω ℱ ).