On a~class of quotient divisible Abelian groups with isomorphic endomorphism semigroups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 121-130.

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Let $\Lambda$ be some class of Abelian groups. We say that a group $A\in\Lambda $ is determined by its endomorphism semigroup $E^\star(A)$ in $\Lambda $ if the isomorphism $E^\star(A)\cong E^\star(B)$, where $B\in\Lambda$, implies $A\cong B$. We describe split Abelian groups in the class $\mathcal{QD}_{\mathrm{cd}}$ of completely decomposable quotient divisible Abelian groups determined by their endomorphism semigroups in the class $\mathcal{QD}_{\mathrm{cd}}$.
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O. V. Lyubimtsev. On a~class of quotient divisible Abelian groups with isomorphic endomorphism semigroups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 121-130. http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a11/

[1] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Abelevy gruppy i ikh koltsa endomorfizmov, Faktorial, M., 2006

[2] Lyubimtsev O. V., “Separabelnye abelevy gruppy bez krucheniya s UA-koltsami endomorfizmov”, Fundament. i prikl. matem., 4:4 (1998), 1419–1422 | MR | Zbl

[3] Lyubimtsev O. V., “Ob opredelyaemosti vpolne razlozhimykh faktorno delimykh abelevykh grupp svoimi polugruppami endomorfizmov”, Izv. vyssh. uchebn. zaved. Matem., 2017, no. 10, 75–82 | MR | Zbl

[4] Puusemp P., “Ob opredelyaemosti periodicheskoi abelevoi gruppy svoei polugruppoi endomorfizmov v klasse vsekh periodicheskikh abelevykh grupp”, Izv. AN EstSSR, Fiz. Mat., 29:3 (1980), 246–253 | MR | Zbl

[5] Sebeldin A. M., “Usloviya izomorfizma vpolne razlozhimykh abelevykh grupp bez krucheniya s izomorfnymi koltsami endomorfizmov”, Matem. zametki, 11:4 (1972), 403–408 | Zbl

[6] Sebeldin A. M., “Ob opredelyaemosti abelevykh grupp svoimi polugruppami endomorfizmov”, Abelevy gruppy i moduli, 1991, 125–134

[7] Fomin A. A., “K teorii faktorno delimykh grupp. I”, Fundament. i prikl. matem., 17:8 (2012), 153–167

[8] Fomin A. A., “K teorii faktorno delimykh grupp. II”, Fundament. i prikl. matem., 20:5 (2015), 157–196

[9] Chandrasekkharan K., Vvedenie v analiticheskuyu teoriyu chisel, Mir, M., 1974 | MR

[10] Beaumont R. A., Pierce R. S., “Torsion-free rings”, Illinois J. Math., 5 (1961), 61–98 | DOI | MR | Zbl

[11] Fomin A. A., Wickless W., “Quotient divisible Abelian groups”, Proc. Amer. Math. Soc., 126:1 (1998), 45–52 | DOI | MR | Zbl