Geodesic
The kernel relation for a strict extension of certain regular semigroups
Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 347-357

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a regular semigroup and denote by (R) its congruence lattice. For , the kernel of pis the set ker . The relation K on (R) defined by λKp if ker λ = ker p is the kernel relation on (R). In general, K is a complete ∩-congruence but it is not a v-congruence. In view of the importance of the kernel-trace approach to the study of congruences on a regular semigroup (the trace of p is its restriction to idempotents of R), it is of considerable interest to determine necessary and sufficient conditions on R in order for K to be a congruence. This being in general a difficult task, one restricts attention to special classes of regular semigroups. For a background on this subject, consult [1]. 
Petrich, Mario. The kernel relation for a strict extension of certain regular semigroups. Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 347-357. doi: 10.1017/S0017089500031785
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