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The kernel relation for an extension of completely 0-simple semigroups

Published online by Cambridge University Press:  19 July 2001

Mario Petrich
Mario Petrich
Affiliation:
Departamento de Algebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
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Abstract

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Let S be an (ideal) extension of a completely 0-simple semigroup S0 by a completely 0-simple semigroup S1. Congruences on S can be uniquely represented in terms of congruences on S0 and S1. In this representation, for a congruence ρ on S, we express ρK,ρT,ρK and ρT, where these denote the least (greatest) congruences with the same kernel (trace) as ρ. Let κ be the least completely 0-simple congruence on S. We provide necessary and sufficient conditions, in terms of the kernel of κ, in order that the relation K be a congruence, and also that [Cscr ](S)/K be a modular lattice, where [Cscr ](S) denotes the congruence lattice of S.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 2 , May 1999 , pp. 211 - 230
Copyright
1999 Glasgow Mathematical Journal Trust