Congruences on semigroups generated by injective nilpotent transformations
M. Paula O. Marques-Smith, Robert Patrick Sullivan · Bulletin of the Australian Mathematical Society · 2006
In 1987, Sullivan characterised the elements of the semigroupNI(X) generated by the nilpotents inI(X), the symmetric inverse semigroup on an infinite setX; and, in the same year, Gomes and Howie did the same for finiteX. In 1999, Marques-Smith and Sullivan determined all the ideals ofNI(X) for arbitraryX. In this paper, we use that work to describe all the congruences onNI(X).