EMBEDDING ℐn IN A 2-GENERATOR INVERSE SUBSEMIGROUP OF ℐn+2
D. B. McAlister, Joseph B. Stephen, Alexei Vernitski · Proceedings of the Edinburgh Mathematical Society · 2002
Abstract Given an integer $n$, we show that $\mathcal{I}_{n}$ embeds in a 2-generated subsemigroup of $\mathcal{I}_{n+2}$, which is an inverse semigroup. An immediate consequence of this result is the following, which is analogous to the case for groups and semigroups: every finite inverse semigroup may be embedded in a finite 2-generated semigroup which is an inverse semigroup. AMS 2000 Mathematics subject classification: Primary 20M18. Secondary 20M20