The monoid of all order-decreasing full transformations

Let Dn be the monoid of all order-decreasing full transformations on n={1,…,n}. In this paper, we determine the maximal subsemigroups as well as the maximal idempotent generated subsemigroups of Dn. Moreover, we characterize the abundance of the maximal (idempotent generated) subsemigroups of Dn. We also characterize the abundance of the ideals of Dn.