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| Title: | Green index and finiteness conditions for semigroups |
| Authors: | Gray, R.
Ruskuc, Nik |
| Keywords: | Finiteness conditions
Index
Residual finiteness
Local finiteness
Complete rewriting-systems
Subsemigroups
Subgroups
Monoids
QA Mathematics |
| Issue Date: | 15-Oct-2008 |
| Citation: | Gray , R & Ruskuc , N 2008 , ' Green index and finiteness conditions for semigroups ' Journal of Algebra , vol 320 , no. 8 , pp. 3145-3164 . |
| Abstract: | Let S be a semigroup and let T be a subsemigroup of S. Then T acts on S by left and by right multiplication. If the complement S \ T has finitely many strong orbits by both these actions we say that T has finite Green index in S. This notion of finite index encompasses subgroups of finite index in groups, and also subsemigroups of finite Rees index (complement). Therefore, the question of S and T inheriting various finiteness conditions from each other arises. In this paper we consider and resolve this question for the following finiteness conditions: finiteness, residual finiteness, local finiteness, periodicity, having finitely many right ideals, and having finitely many idempotents. (c) 2008 Elsevier Inc. All rights reserved. |
| Version: | Postprint |
| Status: | Peer reviewed |
| URI: | http://hdl.handle.net/10023/2144 |
| DOI: | http://dx.doi.org/10.1016/j.jalgebra.2008.07.008 |
| ISSN: | 0021-8693 |
| Type: | Journal article |
| Rights: | This is an author version of this article. The published version (c) 2008 Elsevier Inc. is available at www.sciencedirect.com |
| Appears in Collections: | University of St Andrews Research
Pure Mathematics Research
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