Geodesic
A note on congruences on orthodox semigroups
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 25-30

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C. Eberhart and W. Williams [3] showed that the least inverse semigroup congruence , on an orthodox semigroup S, plays a very important role in determining the structure of the lattice of congruences on S. In this note we show that their results can be applied to give an explicit construction for the idempotent separating congruences on S in terms of idempotent separating congruences on S/. 
McAlister, D. B. A note on congruences on orthodox semigroups. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 25-30. doi: 10.1017/S0017089500005735
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