Congruences on Nilpotent-generated Partial Transformation Semigroups
M. Paula O. Marques-Smith, Robert Patrick Sullivan · Algebra Colloquium · 2009
In 1987, Sullivan characterised the elements of the semigroup NP(X) generated by the nilpotents in P(X), the semigroup (under composition) consisting of all partial transformations of a set X; and in 1999, Marques-Smith and Sullivan determined all the ideals of NP(X) for arbitrary X. In this paper, we use that work to describe all the congruences on NP(X).