Several characterizations for generalized inverses in a ring
Huihui Zhu · Linear and Multilinear Algebra · 2017
Let R be a unital -ring and a, p, q elements of R. When a is regular, and and , we derive the existence criterion and formula of the Moore–Penrose inverses of paq in a ring. Also, we give necessary and sufficient conditions for the existence of the core and dual core inverses of paq. As applications, the existence criterion and the expression of the core and dual core inverses of 2 by 2 matrices over a ring are given.