Radicals Commuting With Bands Of Semigroups

F25.72> y) 2 ae(S) =) (f(x); f(y)) 2 ae(T ) for any homomorphism f : S ! T ; (R2) ae(S=ae(S)) = ' for any s 2 A. Throughout, we shall consider radicals on the class of all semigroups. The congruence ae(S) is called the ae-radical of S. A semigroup S is said to be ae-semisimple (ae-radical) if ae(S) = ' (or ae(S) = !). If it is clear which radical is under consideration, then we shall omit the prefix `ae-'. The class&lt