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.
| Original language | English |
|---|---|
| Pages (from-to) | 311-330 |
| Number of pages | 20 |
| Journal | Czechoslovak Mathematical Journal |
| Volume | 58 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2008 |
Keywords
- Bicyclic monoid
- Subsemigroup
- Generators
- Defining relations
- Automatic structures
- Automatic semigroups
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Dive into the research topics of 'Properties of the subsemigroups of the bicyclic monoid'. Together they form a unique fingerprint.Projects
- 1 Finished
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EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications
Linton, S. (PI), Gent, I. (CoI), Leonhardt, U. (CoI), Mackenzie, A. (CoI), Miguel, I. (CoI), Quick, M. (CoI) & Ruskuc, N. (CoI)
1/09/05 → 31/08/10
Project: Standard
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