Geodesic
Harmonic inverse semigroups
Glasgow mathematical journal, Tome 31 (1989) no. 3, pp. 335-351

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

An inverse semigroup S shall be said to be harmonic if every congruence on S is determined by any one of its classes. In other words, if λ and ρ are congruences on S having a congruence class in common, then λ = ρ. The class of all harmonic semigroups contains all bisimple inverse semigroups, as proved by Žitomirskiĭ [11] and also by Schein [10], and all congruence-free inverse semigroups. Moreover, is contained in the class of all 0-simple or simple inverse semigroups, as is easy to see. We shall show that there exist non-bisimple, non-congruence-free harmonic semigroups and that there are simple inverse semigroups which are not harmonic. 
Petrich, Mario; Rankin, Stuart A. Harmonic inverse semigroups. Glasgow mathematical journal, Tome 31 (1989) no. 3, pp. 335-351. doi: 10.1017/S0017089500007904
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