Geodesic
The group $\operatorname{Hom}(A,B)$ as an Artinian $\operatorname{E}(B)$- or $\operatorname{E}(A)$-module
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 81-96.

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The conditions of Artinianity of the homomorphism group $\operatorname{Hom}(A,B)$ as a module over the endomorphism ring of the Abelian group $B$ or $A$ are found. 
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P. A. Krylov; Y. I. Podberezina. The group $\operatorname{Hom}(A,B)$ as an Artinian $\operatorname{E}(B)$- or $\operatorname{E}(A)$-module. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 81-96. http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a10/

[1] Krylov P. A., Podberezina E. I., “Stroenie smeshannykh abelevykh grupp s neterovymi koltsami endomorfizmov”, Abelevy gruppy i moduli, Tomsk, 1994, 121–129 | MR

[2] Fuks L., Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974

[3] Arnold D. M., Finite Rank Torsion-Free Abelian Groups and Rings, Lect. Notes Math., 931, Springer, 1982 | MR | Zbl

[4] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Endomorphism Rings of Abelian Groups, Kluwer Academic Publishers, Dordrecht, 2003 | MR