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Inverse monoids and rational Schreier subsets of the free group

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Abstract

An inverse monoidM is an idempotent-pure image of the free inverse monoid on a setX if and only ifM has a presentation of the formM=Inv<X:eo=fi, i∈I>, wheree i ,f i are idempotents of the free inverse monoid: every inverse monoid is an idempotent-separating image of one of this type. IfR is anR-class of such an inverse monoid, thenR may be regarded as a Schreier subset of the free group onX. This paper is concerned with an examination of which Schreier subsets arise in this way. In particular, ifI is finite, thenR is a rational Schreier subset of the free group. Not every rational Schreier set arises in this way, but every positively labeled rational Schreier set does.

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Authors and Affiliations

  1. Department of Computer Science, University of Nebraska-Lincoln, 68588, Lincoln, NE, USA

    Stuart W. Marglis & John C. Meakin

  2. Department of Mathematics & Statistics, University of Nebraska-Lincoln, 68588, Lincoln, NE, USA

    Stuart W. Marglis & John C. Meakin

Authors
  1. Stuart W. Marglis
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  2. John C. Meakin
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Additional information

Communicated by G. Lallement

Research supported by National Science Foundation grant #DMS8702019.

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Marglis, S.W., Meakin, J.C. Inverse monoids and rational Schreier subsets of the free group. Semigroup Forum 44, 137–148 (1992). https://doi.org/10.1007/BF02574335

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  • DOI: https://doi.org/10.1007/BF02574335

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