On semigroups of endomorphisms of a chain with restricted range.
For a (possibly infinite) chain \(X\) and a non-empty subset \(Y\) of \(X\) the paper under review studies the semigroup \(O(X,Y)\) of all endomorphisms of \(X\) whose image is contained in \(Y\). The main result of the paper characterizes Green's relations for and characterizes the largest regular subsemigroup in \(O(X,Y)\). For finite chains the authors also classify semigroups \(O(X,Y)\) up to isomorphism and determine their rank.
scientific article; zbMATH DE number 6363659
scientific article