Geodesic
Separable torsion free Abelian groups with $UA$-rings of endomorphisms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1419-1422

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A semigroup $(R,\cdot)$ is said to be a unique addition ring ($UA$-ring) if there exists a unique binary operation $+$, making $(R,\cdot,+)$ into a ring. We call an abelian group $\operatorname{End}$-$UA$-group if its endomorphism ring is $UA$-ring. As a result we have obtained a characterization of separable tortion free $\operatorname{End}$-$UA$-groups. 
@article{FPM_1998_4_4_a17,
     author = {O. V. Ljubimtsev},
     title = {Separable torsion free {Abelian} groups with $UA$-rings of endomorphisms},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1419--1422},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a17/}
}
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O. V. Ljubimtsev. Separable torsion free Abelian groups with $UA$-rings of endomorphisms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1419-1422. http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a17/