Closed inverse subsemigroups of graph inverse semigroups

Amal Saad Alali, Nick Gilbert

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
49 Downloads (Pure)

Abstract

As part of his study of representations of the polycylic monoids, M.V. Lawson described all the closed inverse submonoidsof a polycyclic monoid and classified them up to conjugacy. We show that Lawson's description can be extended to closed inverse subsemigroups of graph inverse semigroups. We then apply B. Schein's theory of cosets in inverse semigroups to the closed inverse subsemigroups of graph inverse semigroups: we give necessary and sufficient conditions for a closed inverse subsemigroup of a graph inverse semigroup to have finite index, and determine the value of the index when it is finite.
Original languageEnglish
Pages (from-to)4667-4678
Number of pages12
JournalCommunications in Algebra
Volume45
Issue number11
Early online date6 Jan 2017
DOIs
Publication statusPublished - 2 Nov 2017

Keywords

  • Inverse semigroup
  • coset
  • graph

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