Geodesic
On weak and $\omega$-high purity in the category of modules
Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 345-356

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In the category of right unitary modules over the associative ring $R$ with $1$, one can define weak $\frak F$ purity, where $\frak F$ is the set of right ideals of $R$ satisfying certain conditions. This is a generalization of the concept of neatness in Abelian group theory. Using the properties of weak $\frak F$-purity, several classes of rings can be characterized. Moreover, an affirmative answer can be given to question 18 [question 14 in the English translation] of A. P. Mishina and L. A. Skornyakov's book “Abelian groups and modules”, which deals with properties of $\omega$-high purity. Groups of weakly $\frak F$-pure and $\omega$-high extensions are studied. Bibliography: 15 titles. 
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     title = {On weak and $\omega$-high purity in the category of modules},
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A. I. Generalov. On weak and $\omega$-high purity in the category of modules. Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 345-356. http://geodesic.mathdoc.fr/item/SM_1978_34_3_a3/