On generalized inverses and Green’s relations

Xavier Mary (1, 2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 FP2M - Fédération Parisienne de Modélisation Mathématique

We 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.

Mots clés: Generalized inverse; Green’s relations; Semigroup

Domaines: Théorie des groupes [math.GR]

Xavier Mary. On generalized inverses and Green’s relations. Linear Algebra and its Applications, 2011, 434 (8), pp.1836-1844. ⟨10.1016/j.laa.2010.11.045⟩. ⟨hal-01366838⟩