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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