On embedding countable sets of endomorphisms
João Araüjo, James D. Mitchell, Nuno Silva · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2003
Sierpi´nski 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 paper we prove 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.