Abstract
We study Abelian groups A with centrally essential endomorphism ring If A is a such group which is either a torsion group or a non-reduced group, then the ring
is commutative. We give examples of Abelian torsion-free groups of finite rank with non-commutative centrally essential endomorphism rings.
Notes
1 It is clear that the ring R with center C is centrally essential if and only if the module RC is an essential extension of the module CC.
2 See 3.1 below.
3 See 3.1 below.
4 cf. [15, Proposition 2.2].
5 A ring is said to be invariant if all its one-sided ideals are ideals.