The congruence lattice of an ideal extension of semigroups
Mario Petrich · Glasgow Mathematical Journal · 1993
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.