Semigroups that are factors of subdirectly irreducible semigroups by their monolith

Jezek and Kepka [4] proved that a universal algebra A with at least one at least binary operation is isomorphic to the factor of a subdirectly irreducible algebra B by its monolith if and only if the intersection of all of its (nonempty) ideals is nonempty, and that B may be chosen to be finite if A is finite. (By an ideal of A is meant a non-empty subset I of A such that f(a(1)_ _a(n)) is an element of I whenever f is an n-ary fundamental operation of A and a(1),...,a(n) is an element of A are elements with a(i) is an element of I for at least one index i.) In the present paper, we prove that if A is a semigroup, then B may be chosen also to be a semigroup, but that a finite semigroup need not be isomorphic to the factor of a finite subdirectly irreducible semigroup by its monolith.