Properties of the subsemigroups of the bicyclic monoid
Luís Descalço, Nik Ruškuc · Czechoslovak Mathematical Journal · 2008
In this paper we study some properties of the subsemigroups of the bicyclic monoid B , by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B .