Vol. LXXX, 1 (2011)
p. 43 - 61

Special congruence triples for a regular semigroup

M. Petrich

Received: June 2, 2009;   Accepted: September 17, 2010

Abstract.   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.

Keywords:  Regular semigroup; congruence lattice; least group congruence; greatest idempotent separating congruence; greatest idempotent pure congruence; least band congruence; relation; implication; independence  

AMS Subject classification: Primary:  20M10  

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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