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| Title: | Generators and relations for subsemigroups via boundaries in Cayley graphs |
| Authors: | Gray, R
Ruskuc, Nik |
| Keywords: | Semigroup
Generators
Presentations
Cayley graph
Subsemigroup
Reidemeister-Schreier rewriting
QA Mathematics |
| Issue Date: | Nov-2011 |
| Citation: | Gray , R & Ruskuc , N 2011 , ' Generators and relations for subsemigroups via boundaries in Cayley graphs ' Journal of Pure and Applied Algebra , vol 215 , no. 11 , pp. 2761-2779 . |
| Abstract: | Given a finitely generated semigroup S and subsemigroup T of S we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if S is finitely generated and T has a finite boundary in S then T is finitely generated. We also prove that if S is finitely presented and T has a finite boundary in S then T is finitely presented. Several corollaries and examples are given. |
| Version: | Postprint |
| Status: | Peer reviewed |
| URI: | http://hdl.handle.net/10023/2131 |
| DOI: | http://dx.doi.org/10.1016/j.jpaa.2011.03.017 |
| ISSN: | 0022-4049 |
| Type: | Journal article |
| Rights: | This is an author version of this article. The definitive version (c) 2011 Elsevier B.V. is available from www.sciencedirect.com |
| Appears in Collections: | University of St Andrews Research
Pure Mathematics Research
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