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| Title: | Properties of the subsemigroups of the bicyclic monoid |
| Authors: | Descalco, L.
Ruskuc, N. |
| Keywords: | Bicyclic monoid
Subsemigroup
Generators
Defining relations
Automatic structures
Automatic semigroups
QA Mathematics |
| Issue Date: | Jun-2008 |
| Citation: | Descalco , L & Ruskuc , N 2008 , ' Properties of the subsemigroups of the bicyclic monoid ' Czechoslovak Mathematical Journal , vol 58 , no. 2 , pp. 311-330 . |
| 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. |
| Version: | Postprint |
| Status: | Peer reviewed |
| URI: | http://hdl.handle.net/10023/2142 |
| DOI: | http://dx.doi.org/10.1007/s10587-008-0018-7 |
| ISSN: | 0011-4642 |
| Type: | Journal article |
| Rights: | This is an author version of this article. The original publication (c)2008 Springer is available at www.springerlink.com |
| Appears in Collections: | University of St Andrews Research
Pure Mathematics Research
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