On endomorphisms of the inverse semigroup of convex order isomorphisms of a bounded rank which are generated by Rees congruences
Olha Popadiuk · Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna · 2022
Let ℐ ω n ( ⃗conv) be the inverse semigroup of convex order isomorphisms of (ω,⩽) of the rank ⩽n. Let 𝔈𝔫𝔡 1 (ℐ ω n ( ⃗conv)) be a subsemigroup of ℐ ω n ( ⃗conv) which consists of 𝔞∈ℐ ω n ( ⃗conv) such that the image (α)𝔞 is isomorphic to a subsemigroup of the semigroup of ω×ω-matrix units for all α∈ℐ ω n ( ⃗conv). We describe the semigroup 𝔈𝔫𝔡(ℐ ω n ( ⃗conv)) of all endomorphisms of the monoid ℐ ω n ( ⃗conv) up to its ideal 𝔈𝔫𝔡 1 (ℐ ω n ( ⃗conv)).