Homomorphisms having a given H-class as a single class
Robert P. Hunter, L. W. Anderson · Journal of the Australian Mathematical Society · 1973
In [1] it was shown if S is a stable semigroup and H an ℋ-class of S then there is a congruence (H) on S in which H is a single class. After considering some consequences of this result for abstract semigroups, we consider some analogous questions for compact semigroups.