Orthogonal completions of the polycyclic monoids

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We introduce the notion of an orthogonal completion of an inverse monoid with zero. We show that the orthogonal completion of the polycyclic monoid on n generators is isomorphic to the inverse monoid of right ideal isomorphisms between the finitely generated right ideals of the free monoid on n generators, and so we can make a direct connection with the Thompson groups Vn,1.

Original languageEnglish
Pages (from-to)1651-1660
Number of pages10
JournalCommunications in Algebra
Issue number5
Publication statusPublished - May 2007


  • Inverse semigroups
  • Thompson groups

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