Geodesic
When Is the Group $\operatorname{Hom}(A,B)$ an Injective $E(B)$-Module?
Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 100-108

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Injectivity conditions for the homomorfism group $\operatorname{Hom}(A,B)$ regarded as a left module over the endomorfism ring of the group $B$ are found for arbitrary Abelian groups $A$ and $B$, where $B$ is nonreduced. 
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     title = {When {Is} the {Group} $\operatorname{Hom}(A,B)$ an {Injective} $E(B)${-Module?}},
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P. A. Krylov; E. G. Pakhomova. When Is the Group $\operatorname{Hom}(A,B)$ an Injective $E(B)$-Module?. Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 100-108. http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a8/