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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |