Geodesic
Properties of the subsemigroups of the bicyclic monoid
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 311-330 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 20M05, 20M10
Keywords: bicyclic monoid; subsemigroup; generators; defining relations; automatic structures 
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     author = {Descal\c{c}o, L. and Ru\v{s}kuc, N.},
     title = {Properties of the subsemigroups of the bicyclic monoid},
     journal = {Czechoslovak Mathematical Journal},
     pages = {311--330},
     year = {2008},
     volume = {58},
     number = {2},
     mrnumber = {2411092},
     zbl = {1166.20052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_2_a1/}
}
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Descalço, L.; Ruškuc, N. Properties of the subsemigroups of the bicyclic monoid. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 311-330. http://geodesic.mathdoc.fr/item/CMJ_2008_58_2_a1/