A ring is an \(E\)-ring if every endomorphism of its additive group is multiplication by a ring element. A ring is an \(A\)-ring if every automorphism of its additive group is multiplication by a ring element. While every \(E\)-ring is obviously an \(A\)-ring, the authors construct an \(A\)-ring which is not an \(E\)-ring. However, they conjecture that all torsion-free \(A\)-rings of finite rank are \(E\)-rings. They show this in many special cases.