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Abstract
In this paper we give a description of all subsemigroups of the bicyclic monoid B. We show that there are essentially five different types of subsemigroups. One of them is the degenerate case, and the remaining four split in two groups of two, linked by the obvious anti-isomorphism of B. Each subsemigroup is characterized by a certain collection of parameters. Using our description, we determine the regular, simple and bisimple subsemigroups of B. Finally we describe algorithms for obtaining the parameters from the generating set.
Original language | English |
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Pages (from-to) | 37-57 |
Number of pages | 21 |
Journal | International Journal of Algebra and Computation |
Volume | 15 |
DOIs | |
Publication status | Published - Feb 2005 |
Keywords
- semigroup
- bicyclic
- subsemigroup
- automatic
- SEMIGROUPS
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Dive into the research topics of '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. A. (PI), Gent, I. P. (CoI), Leonhardt, U. (CoI), Mackenzie, A. (CoI), Miguel, I. J. (CoI), Quick, M. (CoI) & Ruskuc, N. (CoI)
1/09/05 → 31/08/10
Project: Standard