… path semigroup, path algebra, respectively. In this paper, we studied some properties of the
congruence lattice … to-one correspondence between congruences on S and certain algebraic …

… ture of the congruence lattices of semigroups and their relation to the structure of the underlying
semigroup which are … In this way simple semigroups with prescribed type of congruence …

… But also, several new and interesting semigroups have been … ture of a semigroup and the
type of its congruence lattice. Up to … a characterization of such semigroups in the following way: …

… is perfect if and only if it is either (I) a chain of groups, with surjective structure mappings,
or (II) an ideal extension of a Brandt semigroup by such a chain of groups, in such a way that …

… the semigroups under study in order that the congruence lattice be contained in a variety ‘k”
of modular lattices. … seems to be a more natural and adequate way to describe congruences. …

… semigroup. He also proved that the trace relation T (defined in the analogous way) is a complete
congruence on the congruence lattice … of regular semigroup theory and finite semigroup …

… congruences of :~'X-normal semigroups of one-to-one transformations with infinite defects.
Moreover, we embed the lattice … a congruence 0 on S may be associated in a canonical way …

… congruences on the congruence lattice are then explored in some detail. Classes of these
congruences are intervals of the congruence lattice; … we shall show another way to derive the …

… congruences on finite semigroups related to Green’s relations and show that each family of
such congruences … The remaining cases follow from the way the corresponding congruences …

… The main result of this paper shows that the congruence lattice of … on congruence lattices of
a regular semigroup S (the U … One way to analyze the structure of A is through its congruence …