Order-preserving transformations with restricted range: regularity, Green's relations, and ideals.
The paper studies the subsemigroup of the semigroup of all order-preserving transformations of a linearly ordered set \(X\) which consists of all transformations \(\alpha\) whose image belongs to a fixed subset \(Y\) of \(X\) and, additionally, satisfies \(\alpha(X)=\alpha(Y)\). The authors characterize regular elements in this subsemigroup, describe Green's relations and characterize ideals. As an application, the authors show that this semigroup is idempotent generated.
semigroups of order-preserving transformations
scientific article; zbMATH DE number 6494311