Geodesic
Abelian groups as endomorphic modules over their endomorphism ring
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 229-233.

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Let $R$ be an associative ring with a unit and $N$ be a left $R$-module. The set $M_R(N)=\{f\colon N\to N\mid f(rx)=rf(x),\ r\in R,\ x\in N\}$ is a near-ring with respect to the operations of addition and composition and contains the ring $E_R(N)$ of all endomorphisms of the $R$-module $N$. The $R$-module $N$ is endomorphic if $M_R(N)=E_R(N)$. We call an Abelian group endomorphic if it is an endomorphic module over its endomorphism ring. In this paper, we find endomorphic Abelian groups in the classes of all separable torsion-free groups, torsion groups, almost completely decomposable torsion-free groups, and indecomposable torsion-free groups of rank 2. 
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     title = {Abelian groups as endomorphic modules over their endomorphism ring},
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D. S. Chistyakov; O. V. Ljubimtsev. Abelian groups as endomorphic modules over their endomorphism ring. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 229-233. http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a13/

[1] Krylov P. A., Mikhalëv A. V., Tuganbaev A. A., Svyazi abelevykh grupp i ikh kolets endomorfizmov, Tomskii gosudarstvennyi universitet, Tomsk, 2002

[2] Turmanov M. A., “Endochistye podmoduli abelevykh grupp bez krucheniya ranga 2”, Abelevy gruppy i moduli, 1990, no. 9, 119–124 | MR | Zbl

[3] Fuks L., Beskonechnye abelevy gruppy, Mir, M., 1974; 1977 | MR | MR | Zbl

[4] Hausen J., Johnson J. A., “Centralizer near-rings that are rings”, J. Austral. Math. Soc. Ser. A, 59 (1995), 173–183 | DOI | MR | Zbl

[5] Maxson C. J., van der Walt A. P. J., “Centralizer near-rings over free ring modules”, J. Austral. Math. Soc. Ser. A, 50 (1991), 279–296 | DOI | MR | Zbl