Generalized inverses in regular rings

Strong inner and strong reflexive inverses in semiprime rings

“…An element u ∈ R is called a strong reflexive inverse of a ∈ R if u is a strong inner inverse of a and a is a strong inner inverse of u. Note also that a ∈ R is strongly regular if and only if it has a unique reflexive inverse [7,Proposition 3.4].…”