  We study Abelian groups $A$ with centrally essential endomorphism ring
$\text{End}\,A$. If $A$ is a such group which is either a torsion group or a
non-reduced group, then the ring $\text{End}\,A$ is commutative. We give
examples of Abelian torsion-free groups of finite rank with non-commutative
centrally essential endomorphism rings. The paper will appear in Communications
in Algebra.
