Limited Part Of Preserving Transformation Semigroup PO_n, Semigroup

The Subsemigroups of Finite Partial Order - Preserving Transformation SemigroupsAbstract In this paper, We completely obtain the structures and classifications of the maximal subsemigroups, the maximal regular subsemigroups, the maximal idempotent梘enerated subsemigroups and the maximal idempotent ?generated regular subsemigroups of POn, consisting of all partial order - preserving transformations on a finite chain with n element. We also determine the structures of the maximal inverse subsemigroups of the ideals of OIn, the inverse subsemigroup of POn, consisting of all partial order - preserving one ?one maps.