Geodesic
Divisibility of Direct Sums in Torsion Theories
Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 211-214

Voir la notice de l'article provenant de la source Cambridge University Press

Given a hereditary torsion theory on the category Mod R of right R-modules we obtain in this paper necessary and sufficient conditions for the direct sum of a given family of R-modules to be divisible for the torsion theory . Using this criterion we show that if is a family of R-modules having the property that is divisible for every countable subset K ol J then is itself divisible. 
Sarath, B.; Varadarajan, K. Divisibility of Direct Sums in Torsion Theories. Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 211-214. doi: 10.4153/CJM-1976-027-6
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[1] 1. Bland, P. E., Divisible and codivisible modules, Math. Scand. 34 (1974), 153–161. Google Scholar

[2] 2. Dickson, S. E., A torsion theory for abelian categories, Trans. Amer. Math. Soc. 21 (1966), 223–235. Google Scholar

[3] 3. Lambek, J., Torsion theories, additive semantics, and rings of quotients, Lecture notes in Mathematics 177 (Springer-Verlag, 1971). Google Scholar

[4] 4. Sarath, B. and Varadarajan, K., Injectivity of direct sums, Comm. Algebra 1 (1974), 517–530. Google Scholar

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