Geodesic
On the nilpotent ranks of certain semigroups of transformations
Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 1-9

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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 bywhere {i} = Xn∖dom α and {j} = Xn∖im α. 
Garba, G. U. On the nilpotent ranks of certain semigroups of transformations. Glasgow mathematical journal, Tome 36 (1994) no. 1, pp. 1-9. doi: 10.1017/S0017089500030482
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