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2002•Proceedings of the Edinburgh Mathematical SocietyOpen access

EMBEDDING ℐn IN A 2-GENERATOR INVERSE SUBSEMIGROUP OF ℐn+2

D. B. McAlister, J. B. Stephen, Alexei Vernitski

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Abstract

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

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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

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Available abstract

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

Key concepts: Inverse semigroup, Semigroup, Mathematics, Inverse, Embedding, Generator (circuit theory), Bicyclic semigroup, Regular semigroup

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