Geodesic
Certain classes of Abelian groups
Sbornik. Mathematics, Tome 12 (1970) no. 2, pp. 213-220 
V. S. Rokhlina. Certain classes of Abelian groups. Sbornik. Mathematics, Tome 12 (1970) no. 2, pp. 213-220. http://geodesic.mathdoc.fr/item/SM_1970_12_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The notions of $\varepsilon$-purity, $\varepsilon$-injectivity, and $\varepsilon$-projectivity are introduced as generalizations of the notions of purity, injectivity, and projectivity in the theory of Abelian groups. The basic result is a description of the $\varepsilon$-purity of the classes of all $\varepsilon$-injective and $\varepsilon$-projective Abelian groups (Propositions 1–6). There is also a description of the classes of $\varepsilon$-divisible and $\varepsilon$-flat Abelian groups. Bibliography: 7 titles.

[1] A. G. Kurosh, Teoriya trupp, Nauka, Moskva, 1967 | MR | Zbl

[2] A. P. Mishina, L. A. Skornyakov, Abelevy gruppy i moduli, Nauka, Moskva, 1969 | MR | Zbl

[3] L. Fuchs, Abelian groups, Budapest, 1967

[4] V. C. Rokhlina, “Zametki ob $\varepsilon$-chistote”, Trudy X Vsesoyuznogo kollokviuma po obschei algebre, t. II, Novosibirsk, 1969, 36–37

[5] D. K. Harrison, J. M. Irwin, C. L. Peercy, E. A. Walker, “High extensions of abelian groups”, Acta Math. Hung., 14:3–4 (1963), 319–330 | MR | Zbl

[6] D. K. Harrison, “Infinite abelian groups and homological methods”, Ann. Math., 69 (1959), 366–361 | DOI | MR

[7] E. A. Walker, “Torsion endomorphic images of mixed abelian groups”, Pacif. J. Math., 11 (1961), 375–377 | MR | Zbl