Subsemigroups of the bicyclic monoid

L Descalco, Nikola Ruskuc

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


In this paper we give a description of all subsemigroups of the bicyclic monoid B. We show that there are essentially five different types of subsemigroups. One of them is the degenerate case, and the remaining four split in two groups of two, linked by the obvious anti-isomorphism of B. Each subsemigroup is characterized by a certain collection of parameters. Using our description, we determine the regular, simple and bisimple subsemigroups of B. Finally we describe algorithms for obtaining the parameters from the generating set.

Original languageEnglish
Pages (from-to)37-57
Number of pages21
JournalInternational Journal of Algebra and Computation
Publication statusPublished - Feb 2005


  • semigroup
  • bicyclic
  • subsemigroup
  • automatic


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