On the nilpotent ranks of certain semigroups of transformations
G. U. Garba · Glasgow Mathematical Journal · 1994
Let Pn be the semigroup of all partial transformations on the set Xn = {1,…, n}. As usual, we shall say that an element α in Pn is of type (k, r) or belongs to the set [k, r] if |dom α|=k and |lim α|. The completion α* of an element α ∈ [n − 1, n − 1] is an element in [n, n] defined by where {i} = Xn∖dom α and {j} = Xn∖im α.