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.