Properties of the subsemigroups of the bicyclic monoid
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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.
Descalco , L & Ruskuc , N 2008 , ' Properties of the subsemigroups of the bicyclic monoid ' , Czechoslovak Mathematical Journal , vol. 58 , no. 2 , pp. 311-330 . https://doi.org/10.1007/s10587-008-0018-7
Czechoslovak Mathematical Journal
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