Outer inverses, minus partial orders, and triplet invariance

Abstract

In the paper, we obtain an explicit formula for the outer inverses of a regular element in an arbitrary ring. It becomes calculable for outer inverses. We characterize the triplet ba − c (resp. ba + c ) invariant under all inner inverses a − (resp. reflexive inverses a + ) of a in a semiprime ring. It is also proved that if R is a regular ring and a, b, c ∈ R, then the triplet bâc is invariant under all outer inversesâ of a if