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On an axiomatic description of weak purities in the category of modules
Sbornik. Mathematics, Tome 37 (1980) no. 1, pp. 71-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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A class of purities that is a generalization of weak purity to the category of modules is studied. A one-to-one correspondence is established between these purities and certain classes of modules, and an intrinsic description of such purities is given, as well as the corresponding classes of modules. A description is also presented with the aid of sets of right ideals of a ring. Bibliography: 10 titles. 
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A. I. Generalov. On an axiomatic description of weak purities in the category of modules. Sbornik. Mathematics, Tome 37 (1980) no. 1, pp. 71-82. http://geodesic.mathdoc.fr/item/SM_1980_37_1_a4/

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[3] A. A. Manovtsev, “Ob additivnykh chistotakh v abelevykh gruppakh”, Trudy XXV nauchn.-tekhn. konf., sekts. matem., MIRZA, 1976, 107–111

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[7] V. Kuzminov, “O proizvodnykh funktorakh proektivnogo predela”, Sib. matem. zh., 8:2 (1967), 333–345 | MR

[8] A. I. Generalov, “O slaboi i $\omega$-vysokoi chistotakh v kategorii modulei”, Matem. sb., 105(147) (1978), 389–402 | MR | Zbl

[9] A. I. Kashu, “Zamknutye klassy levykh $\Lambda$-modulei i zamknutye mnozhestva idealov koltsa $\Lambda$”, Matem. zametki, 5:3 (1969), 381–390 | Zbl

[10] G. Reneult, “Étude de certains anneaux $A$ liés aux sous-modules compléments d'un $A$-module”, C. r. Acad, scient. Paris, 259:23 (1964), A4203–A4205