Geodesic
The congruence lattice of an ideal extension of semigroups
Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 39-50

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

Let S be an ideal of a semigroup V. In such a case, V is an (ideal) extension of S by T = V/S. The problem considered in [2] is the construction of all congruences on V in terms of congruences on S and T. This did not succeed for all congruences but it did for those congruences whose restriction to S is weakly reductive. If the extension is strict, more precise constructions are also given there. With some relatively weak restrictions on S, we are able to obtain in this way all congruences on V in the form indicated above. 
Petrich, Mario. The congruence lattice of an ideal extension of semigroups. Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 39-50. doi: 10.1017/S001708950000954X
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[1] 1.Clifford, A. H., Extensions of semigroups, Trans. Amer. Math. Soc. 68 (1950), 165–173. Google Scholar | DOI

[2] 2.Petrich, M., Congruences on extensions of semigroups, Duke Math. J. 34 (1967), 215–224. Google Scholar | DOI

[3] 3.Petrich, M., Inverse semigroups (Wiley-Interscience, New York, 1984). Google Scholar

[4] 4.Petrich, M., The congruence lattice of an extension of completely 0-simple semigroups (preprint). Google Scholar

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