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Special congruence triples for a regular semigroup

Author(s): M. Petrich

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXX;
Issue: 1;
Start page: 43;
Date: 2011;
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Keywords: Regular semigroup | congruence lattice | least group congruence | greatest idempotent separating congruence | greatest idempotent pure congruence | least band congruence | relation | implication | independence

With the usual notation for congruences on a regular semigroup S, in a previous communication we studied the lattice Λ generated by Γ = {σ, τ, μ, β} relative to properties such as distributivity and similar conditions. For K and T the kernel and trace relations on the congruence lattice of S, we form an abstraction of the triple (Λ; K|Λ, TΛ) called a c-triple. In this study appear a number of relations on the free lattice generated by Γ. Here we study implications and independence of these relations, both on c-triples as well as on congruence lattices of regular semigroups. We consider the behavior of the members of Γ under forming of finite direct products, construct examples, and supplement some results in the paper referred to above.
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