On the Semigroup of Injective Endomorphisms of the Semigroup BωFn Generated by the Family Fn of Initial Finite Intervals in ω

We describe injective endomorphisms of the inverse semigroup B ω F introduced in [ Visn. Lviv. Univ., Ser. Mech.-Mat., Issue 90, 5 (2020)] for the case where the family F n is generated by the set {0,1,…, n }. In particular, it is shown that the semigroup of injective endomorphisms of the semigroup B ω F is isomorphic to (ω, +). Moreover, we describe the structure of the semigroup E n d B λ of all endomorphisms of the semigroup of λ × λ -matrix units B λ .