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Congruence lattices of regular semigroups related to kernels and traces

Published online by Cambridge University Press:  20 January 2009

Mario Petrich
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The kernel–trace approach to congruences on a regular semigroup S can be refined by introducing the left and right traces. This induces eight operators on the lattice of congruences on S: t1, k, tr,; Tt, K, Tr; t, T. We describe the lattice of congruences on S generated by six 3-element subsets of the set {ωt1, ωk, ωtr, εTt, εK, εTr} where ω and ε denote the universal and the equality relations. This is effected by means of a diagram and in terms of generators and relations on a free distributive lattice, or a homomorphic image thereof. We perform the same analysis for the lattice of congruences on S generated by the set {εK, ωk, εT, ωt}.

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Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 179 - 203
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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