Geodesic
Congruences on a bisimple ω-semigroup
Glasgow mathematical journal, Tome 7 (1966) no. 4, pp. 184-192

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In a semigroup S the set E of idempotents is partially ordered by the rule that e≦ƒ if and only if eƒ=e=ƒe. We say that S is an ω-semigroup if E={ei: i=0, 1, 2, ...}, whereBisimple ω-semigroups have been classified in [10]. From a group G and an endomorphism α of G a bisimple ω-semigroup S(G, α) can be constructed by a process described below in § 1: moreover, any bisimple ω-semigroup is isomorphic to one of this type. 
Munn, W. D.; Reilly, N. R. Congruences on a bisimple ω-semigroup. Glasgow mathematical journal, Tome 7 (1966) no. 4, pp. 184-192. doi: 10.1017/S2040618500035413
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