Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T20:18:25.647Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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