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Properties of the subsemigroups of the bicyclic monoid

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Aveiro, 3810-193, Aveiro, Portugal

    L. Descalço & N. Ruškuc

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  1. L. Descalço
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  2. N. Ruškuc
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Descalço, L., Ruškuc, N. Properties of the subsemigroups of the bicyclic monoid. Czech Math J 58, 311–330 (2008). https://doi.org/10.1007/s10587-008-0018-7

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  • DOI: https://doi.org/10.1007/s10587-008-0018-7

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