Geodesic
Bicommutators of fully divisible modules
Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 431-440 
A. I. Kashu. Bicommutators of fully divisible modules. Sbornik. Mathematics, Tome 29 (1976) no. 4, pp. 431-440. http://geodesic.mathdoc.fr/item/SM_1976_29_4_a0/
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     author = {A. I. Kashu},
     title = {Bicommutators of fully divisible modules},
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     volume = {29},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_4_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the module $M_R$, injective with respect to the pair $R/K\subseteq E(R/K)$, where $K=0:M$, and form the ring $Q_M (R)$ by constructing rings of quotients with respect to torsion. We find necessary and sufficient conditions on $M_R$ for $Q_M (R)$ to coincide with the bicommutator of $M_R$. Among the consequences of this are the well-known results of Beachy and Morita on bicommutators of coexact fully divisible modules and of injective endofinite modules. Bibliography: 7 titles.

[1] J. Lambek, Torsion theories, additive semantics and rings of quotients, Lecture Notes Math., 177, Springer-Verlag, Berlin–Heidelberg–New York, 1971 | MR

[2] K. Morita, “Localizations in categories of modules, I”, Math. Z., 144:2 (1970), 121–144 | DOI | MR | Zbl

[3] K. Morita, “Flat modules, injective modules and quotient rings”, Math. Z., 120:1 (1971), 25–40 | DOI | MR | Zbl

[4] J. A. Beachy, “Bicommutators of cofaithfull, fully divisible modules”, Canad. J. Math., 23:2 (1971), 202–213 | MR

[5] J. A. Beachy, “Generating and cogenerating structures”, Trans. Amer. Math. Soc., 158:1 (1971), 75–92 | DOI | MR | Zbl

[6] O. Goldman, “Rings and modules of quotients”, J. Algebra, 13:1 (1969), 10–47 | DOI | MR | Zbl

[7] A. I. Kashu, “Kogda radikal, assotsiirovannyi modulyu, yavlyaetsya krucheniem?”, Matem. zametki, 16:1 (1974), 41–48 | Zbl