Generalized inverses modulo ℋ in semigroups and rings
Xavier Mary, Pedro Henrique de Bitencourt Patricio · Linear and Multilinear Algebra · 2012
The definition of the inverse along an element was very recently introduced, and it contains known generalized inverses such as the group, Drazin and Moore–Penrose inverses. In this article, we first prove a simple existence criterion for this inverse in a semigroup, and then relate the existence of such an inverse in a ring to the ring units.