Geodesic
Nonreduced Abelian Groups with $\mathrm{UA}$-Rings of Endomorphisms
Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 425-429 Cet article a éte moissonné depuis la source Math-Net.Ru

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A ring $K$ is a unique addition ring (a $\mathrm{UA}$-ring) if its multiplicative semigroup $(K,\,\cdot\,)$ can be equipped with a unique binary operation $+$ transforming this semigroup to a ring $(K,\,\cdot\,,+)$. An Abelian group is called an $\operatorname{End}$-$\mathrm{UA}$-group if its endomorphism ring is a $\mathrm{UA}$-ring. In the paper, we find $\operatorname{End}$-$\mathrm{UA}$-groups in the class of nonreduced Abelian groups.
Keywords: Abelian group, endomorphism ring. 
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     author = {O. V. Ljubimtsev},
     title = {Nonreduced {Abelian} {Groups} with~$\mathrm{UA}${-Rings} of {Endomorphisms}},
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O. V. Ljubimtsev. Nonreduced Abelian Groups with $\mathrm{UA}$-Rings of Endomorphisms. Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 425-429. http://geodesic.mathdoc.fr/item/MZM_2017_101_3_a8/

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