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The Bergman property for semigroups

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bergman7.pdf (252.0Kb)
Date
08/2009
Author
Maltcev, V.
Mitchell, J. D.
Ruskuc, N.
Funder
EPSRC
Grant ID
EP/C523229/1
Keywords
Finitary power semigroups
Generating countable sets
Uncountable cofinalities
Infinite
Transformations
Endomorphisms
Monoids
Ranks
QA Mathematics
Metadata
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Abstract
In this article, we study the Bergman property for semigroups and the associated notions of cofinality and strong cofinality. A large part of the paper is devoted to determining when the Bergman property, and the values of the cofinality and strong cofinality, can be passed from semigroups to subsemigroups and vice versa. Numerous examples, including many important semigroups from the literature, are given throughout the paper. For example, it is shown that the semigroup of all mappings on an infinite set has the Bergman property but that its finitary power semigroup does not; the symmetric inverse semigroup on an infinite set and its finitary power semigroup have the Bergman property; the Baer-Levi semigroup does not have the Bergman property.
Citation
Maltcev , V , Mitchell , J D & Ruskuc , N 2009 , ' The Bergman property for semigroups ' , Journal of the London Mathematical Society , vol. 80 , no. 1 , pp. 212-232 . https://doi.org/10.1112/jlms/jdp025
Publication
Journal of the London Mathematical Society
Status
Peer reviewed
DOI
https://doi.org/10.1112/jlms/jdp025
ISSN
0024-6107
Type
Journal article
Rights
This is an author version of this article. The published version, (c) 2009 London Mathematical Society, is available from Oxford Journals at doi: 10.1112/jlms/jdp025
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  • University of St Andrews Research
URL
http://www.scopus.com/inward/record.url?scp=68349128462&partnerID=8YFLogxK
URI
http://hdl.handle.net/10023/2145

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