A classification of disjoint unions of two or three copies of the free monogenic semigroup

摘要

We prove that, up to isomorphism and anti-isomorphism, there are only two types of semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine types of semigroups which are the union of three copies of the free monogenic semigroup. We provide finite presentations for semigroups of each of these types.