Semigroups generated by nilpotent transformations

In a seminal paper published in 1966, John Howie characterised the elements of _x, the semigroup (under composition) of all total transformations of a set X into itself, which can be written as a product of idempotents in _x. We now initiate the study of the subsemigroup of _x, the semigroup of all partial transformations of X, which is generated by the nilpotents of _x