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Idempotent-generated semigroups and pseudovarieties

Part of: Semigroups

Published online by Cambridge University Press:  20 June 2011

J. Almeida  and
A. Moura
J. Almeida
Affiliation:
Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal ([email protected])
A. Moura
Affiliation:
Laboratório de Engenharia Matemática, Instituto Superior de Engenharia do Porto, Rua Dr António Bernardino de Almeida 431, 4200-072 Porto, Portugal and Centro de Matemática, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal ([email protected])
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Abstract

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The operator that constructs the pseudovariety generated by the idempotent-generated semi-groups of a given pseudovariety is investigated. Several relevant examples of pseudovarieties generated by their idempotent-generated elements are given, as well as some properties of this operator. Particular attention is paid to the pseudovarieties in {J, R, L, DA} concerning this operator and their generator ranks and idempotent-generator ranks.

Keywords

finite semigrouppseudovarietyoperatoridempotent-generated semigroupgenerator rankidempotent generator rank

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 545 - 568
Copyright
Copyright © Edinburgh Mathematical Society 2011

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