Resumo: We study generalized inverses on semigroups by means of Green's
relations. We define a new generalized inverse, the inverse along an
elemento and study its properties. In particular we show that the
classical generalized inverses (group inverse, Drazin inverse and
Moore-Penrose inverse) belong to this class. We then show that this
notion of invertibility can be interpreted as a kind of invertibility
modulo Green's relation H. |