SUBSEMIGROUPS OF THE BICYCLIC MONOID
Luís Descalço, Nik Ruškuc · International Journal of Algebra and Computation · 2005
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.