Geodesic
Abelian Groups as $\mathrm{UA}$-Modules over Their Endomorphism Ring
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 934-941.

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Suppose that $V$ is a module over a ring $R$. The module $V$ is called a unique addition module ($\mathrm{UA}$-module) if it is not possible to change the addition on the set $V$ without changing the action of $R$ on $V$. In this paper, we find Abelian groups that are $\mathrm{UA}$-modules over their endomorphism ring.
Mots-clés : unique addition module, torsion-free group
Keywords: Abelian group, quasidecomposition of a group, distributive module, irreducible module, uniserial module, endomorphism ring. 
@article{MZM_2012_91_6_a13,
     author = {D. S. Chistyakov},
     title = {Abelian {Groups} as $\mathrm{UA}${-Modules} over {Their} {Endomorphism} {Ring}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {91},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a13/}
}
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D. S. Chistyakov. Abelian Groups as $\mathrm{UA}$-Modules over Their Endomorphism Ring. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 934-941. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a13/

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