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

Published online by Cambridge University Press:  05 February 2002

D. B. McAlister ,
J. B. Stephen  and
A. S. Vernitski
D. B. McAlister
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
J. B. Stephen
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
A. S. Vernitski
Affiliation:
School of Computing Science, Middlesex University, London N11 2NQ, UK
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Abstract

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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

Keywords

inverse semigroupsgenerators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 1 - 4
Copyright
Copyright © Edinburgh Mathematical Society 2002