Embedding countable sets of endomorphisms

Sierpinski proved that every countable set of mappings on an infinite set X is contained in a 2-generated subsemigroup of the semigroup of all mappings on X. In this talk we discuss a generalisation of this result to semigroups of endomorphisms. We show that every countable set of endomorphisms of an algebra A which has an infinite basis (independent generating set) is contained in a 2-generated subsemigroup of the semigroup of all endomorphisms of A.