On the Monoid of All Partial Order-Preserving Extensive Transformations

A partial transformation α on an n-element chain X _n is called order-preserving if x ≤ y implies xα ≤yα for all x, y in the domain of α and it is called extensive if x ≤ xα for all x in the domain of α. The set of all partial order-preserving extensive transformations on X _n forms a semiband POE _n . We determine the maximal subsemigroups as well as the maximal subsemibands of POE _n .