Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\)

Abstract

The semigroups of all increasing functions over \(\mathbb{N}\) and  \(\mathbb{Z}\)  are considered. It is shown that both these semigroups do not admit an irreducible system of generators. In their subsemigroups of cofinite functions all irreducible systems of generators are described. The last semigroups are presented in terms of generators and relations.