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Congruence networks for completely simple semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Mario Petrich
Mario Petrich
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A156, Canada
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Abstract

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The operators K, k, T and t are defined on the lattice of congruences on a Rees matrix semigroup S as follows. For ρ ∈ (S), ρK and ρk (ρT and ρt) are the greatest and the least congruences with the same kernel (trace) as ρ, respectively. We determine the semigroup generated by the operators K, k, T and t as they act on all completely simple semigroups. We also determine the network of congruences associated with a congruence ρ ∈ (S) and the lattice generated by it. The latter is then represented by generators and relations.

MSC classification

Secondary: 20M10: General structure theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 2 , April 1994 , pp. 243 - 266
Copyright
Copyright © Australian Mathematical Society 1994

References

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