Regularity and Green’s relations for semigroups of transformations preserving a zigzag order and an equivalence
Thanakorn Prinyasart, Ratana Srithus, Chaleamrach Malangpoo · Asian-European Journal of Mathematics · 2023
Consider a finite ordered set [Formula: see text] whose order forms a zigzag. For an equivalence [Formula: see text] on [Formula: see text], let [Formula: see text] be the set of all order homomorphism preserving [Formula: see text]. In this paper, we completely describe the regularity of elements and Green’s relations for [Formula: see text] under a certain condition.