**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. LXXVI, 2 (2007)

p. 201 - 214

A Special Congruence Lattice of a Regular Semigroup

M. Petrich

**Abstract**.
Let *S* be a regular semigroup and **C** its lattice of
congruences. We consider the sublattice L of
**C** generated by s-the least group,
t-the
greatest idempotent pure, m-the greatest idempotent
separating and b-the least band congruence on *S*. To this
end, we study the following special cases: (1) any three of these
congruences generate a distributive lattice, (2) L is
distributive, (3) the restriction of the *K*-relation to
L is a congruence and (4) a further special case. In each
of these instances, we provide several characterizations. Our
basic concept is that of a *c*-triple which represents an
abstraction of (L;
*K*|_{L},
*T*|_{L}).

**Keywords:**
regular semigroups, congruence lattice, least group
congruence, greatest idempotent pure congruence, greatest
idempotent separating congruence, least band congruence.

**AMS Subject classification.** Primary: 20M10.

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