Certain classes of Abelian groups

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.