Geodesic
Abelian Groups as $\mathrm{UA}$-Modules over the Ring~$\mathbb Z$
Matematičeskie zametki, Tome 87 (2010) no. 3, pp. 412-416

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Let $V$ be a module over a ring $R$. The module $V$ is called a unique addition module (a $\mathrm{UA}$-module) if there is no new addition on the set $V$ without changing the action of $R$ on $V$. In the paper, the $\mathrm{UA}$-modules over the ring $\mathbb Z$ are found.
Keywords: unitary module over an associative ring, mixed Abelian group, strongly servant subgroup, reduced group.
Mots-clés : unique addition module, divisible group 
@article{MZM_2010_87_3_a8,
     author = {O. V. Ljubimtsev and D. S. Chistyakov},
     title = {Abelian {Groups} as $\mathrm{UA}${-Modules} over the {Ring~}$\mathbb Z$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {412--416},
     publisher = {mathdoc},
     volume = {87},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_3_a8/}
}
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O. V. Ljubimtsev; D. S. Chistyakov. Abelian Groups as $\mathrm{UA}$-Modules over the Ring~$\mathbb Z$. Matematičeskie zametki, Tome 87 (2010) no. 3, pp. 412-416. http://geodesic.mathdoc.fr/item/MZM_2010_87_3_a8/