The maximal idempotent-generated subsemigroup of partial order-preserving transformation semigroups generated by squasi-idempotents

Let n = \ 1,2, \cdots ,n\ be a set ordered in the standard way, and let PO_n be the partial order-preserving semigroup on n . Let \alpha \in PO_n , If \alpha ^2 = \alpha , then \alpha is an idempotent element. Thus we call that \alpha is a squasi-idempotent element if \alpha ^2 \ne \alpha and \alpha ^2 is an idempotent element. We study the maximal subsemigroups and square idempotent elements of semigroup PO_n , and provided the structure and complete classification of the maximal idempotent generating subsemigroup of PO_n ( n \geqslant 5 ) by the squasi-idempotents.