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}, T_{Λ}) 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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