On disjoint unions of finitely many copies of the free monogenic semigroup

TL;DR

This paper proves that semigroups formed by finitely many disjoint copies of the natural numbers under addition are finitely presented and residually finite, highlighting their algebraic structure and properties.

Contribution

It establishes that such semigroups are finitely presented and residually finite, providing new insights into their algebraic characteristics.

Findings

Semigroups as finite disjoint unions of natural numbers are finitely presented.

These semigroups are residually finite.

The paper characterizes the algebraic structure of these semigroups.

Abstract

Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.