2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222830We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose inverse) belong to this class.Group TheoryFunctional Analysis15A09; 20M99text