Abstract
In this paper, three theorems are proven on the separability of torsion and pretorsion in the category of right Λ-modules. It follows from Theorem 2 that each non-trivial torsion and pretorsion in Abelian groups is inseparable. The theorems are accompanied by examples. The bibliography contains three titles.
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L. Ioffe, Radical Modules, Sib. Matem. zh.,5, No. 4, 820–825 (1964).
I. A. Rotmann, A characterization of fields among integral domains, Anais Acad. brasil. cienc.,32, No. 2, 193–194 (1960).
Y. M. Maranda, Injective structures, Trans. Amer. Math. Soc,110, No. 1, 98–135 (1964).
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Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 681–688, December, 1967.
The author wishes to thank L. A. Skornyakov for directing this work.
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Gorbachuk, E.L. Separability of torsion and pretorsion in the category of right Λ -modules. Mathematical Notes of the Academy of Sciences of the USSR 2, 901–905 (1967). https://doi.org/10.1007/BF01473475
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DOI: https://doi.org/10.1007/BF01473475