The congruences on the semigroup of balanced transformations of an infinite set

In 1966, Howie showed that the semigroup generated by all nonidentity idempotent transformations of an infinite set X is the disjoint union of two semigroups, one of which is denoted by H and consists of all balanced transformations of X (that is, all transformations whose defect, shift and collapse are equal and infinite). Subsequently, Howie (1981) and Marques (1983) showed that certain Rees quotient semigroups associated with H are congruence-free. Here, we describe all congruences on H.Fundação para a Ciência e a Tecnologia (FCT).Centro de matemática da Universidade do Minho