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Title: The Bergman property for semigroups
Authors: Maltcev, V.
Mitchell, J. D.
Ruskuc, N.
Keywords: Finitary power semigroups
Generating countable sets
Uncountable cofinalities
Infinite
Transformations
Endomorphisms
Monoids
Ranks
QA Mathematics
Issue Date: Aug-2009
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 .
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.
Version: Postprint
Status: Peer reviewed
URI: http://hdl.handle.net/10023/2145
DOI: http://dx.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
Appears in Collections:Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
University of St Andrews Research
Pure Mathematics Research



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