The Bergman property for semigroups

V. Maltcev; J. D. Mitchell; N. Ruskuc

doi:10.1112/jlms/jdp025

The Bergman property for semigroups

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	212-232
Number of pages	21
Journal	Journal of the London Mathematical Society
Volume	80
Issue number	1
Early online date	10 Jun 2009
DOIs	https://doi.org/10.1112/jlms/jdp025
Publication status	Published - Aug 2009

Keywords

Finitary power semigroups
Generating countable sets
Uncountable cofinalities
Infinite
Transformations
Endomorphisms
Monoids
Ranks

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10.1112/jlms/jdp025

Bergman7
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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Cite this

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T1 - The Bergman property for semigroups

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AU - Mitchell, J. D.

AU - Ruskuc, N.

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KW - Finitary power semigroups

KW - Generating countable sets

KW - Uncountable cofinalities

KW - Infinite

KW - Transformations

KW - Endomorphisms

KW - Monoids

KW - Ranks

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The Bergman property for semigroups

Abstract

Keywords

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EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

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The Bergman property for semigroups

Abstract

Keywords

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EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

Cite this