1. Properties of the subsemigroups of the bicyclic monoid
- Creator:
- Descalço, L. and Ruškuc, N.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- bicyclic monoid, subsemigroup, generators, defining relations, and automatic structures
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public