Set Products in Transformation Semigroups (Peter Higgins, NBSAN Heriot-Watt, 23rd July 2009)

Abstract: We describe products of arbitrary L- R- and H-classes with the set E of idempotents of a full transformation semigroup. The description involves a new parameter and the key condition on which membership revolves can be expressed as an equation. Unexpected corollaries include the fact that EH is a subsemigroup (and a union of H-classes) for any H-class H of a finite full transformation semigroup, a result that does not hold in general.