Geodesic
Torsion Abelian afi-groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 139-145.

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This paper is devoted to the study of Abelian afi-groups. A subgroup $A$ of an Abelian group $G$ is called its absolute ideal if $A$ is an ideal of any ring on $G$. We will call an Abelian group an afi-group if all of its absolute ideals are fully invariant subgroups. In this paper, we will describe afi-groups in the class of fully transitive torsion groups (in particular, separable torsion groups) and divisible torsion groups. 
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Pham Thi Thu Thuy. Torsion Abelian afi-groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 8, pp. 139-145. http://geodesic.mathdoc.fr/item/FPM_2012_17_8_a13/

[1] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1977

[2] Fuks L., Beskonechnye abelevy gruppy, v. 2, Mir, M., 1977

[3] Chekhlov A. R., “Ob abelevykh gruppakh, vse podgruppy kotorykh yavlyayutsya idealami”, Vestn. Tomsk. gos. un-ta. Mat. i mekh., 2009, no. 3, 64–67

[4] Fried E., “On the subgroups of Abelian groups that are ideals in every ring”, Proc. Colloq. Abelian Groups, Budapest, 1964, 51–55 | MR | Zbl