Geodesic
A Special Congruence Lattice of a Regular Semigroup
Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 2 
M. Petrich. A Special Congruence Lattice of a Regular Semigroup. Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a8/
@article{AMUC_2007_76_2_a8,
     author = {M. Petrich},
     title = {A {Special} {Congruence} {Lattice} of a {Regular} {Semigroup}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2007},
     volume = {76},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2007_76_2_a8/}
}
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Voir la notice de l'article provenant de la source Comenius University

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 ).