Geodesic
Torsion-Free Modules with $\mathrm{UA}$-Rings of Endomorphisms
Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 898-906

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An associative ring $R$ is called a unique addition ring ($\mathrm{UA}$-ring) if its multiplicative semigroup $(R,\,\cdot\,)$ can be equipped with a unique binary operation $+$ transforming the triple $(R,\,\cdot\,,+)$ to a ring. An $R$-module $A$ is said to be an $\mathrm{End}$-$\mathrm{UA}$-module if the endomorphism ring $\mathrm{End}_R(A)$ of $A$ is a $\mathrm{UA}$-ring. In the paper, the torsion-free $\mathrm{End}$-$\mathrm{UA}$-modules over commutative Dedekind domains are studied. In some classes of Abelian torsion-free groups, the Abelian groups having $\mathrm{UA}$-endomorphism rings are found.
Mots-clés : Abelian torsion-free group, $\mathrm{End}$-$\mathrm{UA}$-module
Keywords: $\mathrm{UA}$-ring, $\mathrm{UA}$-endomorphism ring. 
@article{MZM_2015_98_6_a9,
     author = {O. V. Ljubimtsev and D. S. Chistyakov},
     title = {Torsion-Free {Modules} with $\mathrm{UA}${-Rings} of {Endomorphisms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {898--906},
     publisher = {mathdoc},
     volume = {98},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a9/}
}
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O. V. Ljubimtsev; D. S. Chistyakov. Torsion-Free Modules with $\mathrm{UA}$-Rings of Endomorphisms. Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 898-906. http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a9/