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Title: Properties of the subsemigroups of the bicyclic monoid
Authors: Descalco, L.
Ruskuc, Nik
Keywords: Bicyclic monoid
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 . , 10.1007/s10587-008-0018-7
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
ISSN: 0011-4642
Type: Journal article
Rights: This is an author version of this article. The original publication (c)2008 Springer is available at
Appears in Collections:Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
Mathematics & Statistics Research
University of St Andrews Research
Pure Mathematics Research

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