Cotorsion Theories and Colocalization

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<jats:p>Let <jats:italic>R</jats:italic> be an associative ring with unit element. Mod-<jats:italic>R</jats:italic> and <jats:italic>R</jats:italic>-Mod will denote the categories of unitary right and left <jats:italic>R</jats:italic>-modules, respectively, and all modules are assumed to be in Mod-<jats:italic>R</jats:italic> unless otherwise specified. For all <jats:italic>M, N ϵ</jats:italic> Mod-<jats:italic>R</jats:italic>, <jats:italic>Hom<jats:sub>R</jats:sub>(M, N)</jats:italic> will usually be abbreviated as <jats:italic>[M, N].</jats:italic> For the definitions of basic terms, and an exposition on torsion theories in Mod-<jats:italic>R</jats:italic>, the reader is referred to Lambek [6]. Jans [5] has called a class of modules which is closed under submodules, direct products, homomorphic images, group extensions, and isomorphic images a <jats:italic>TTF</jats:italic> (torsion-torsionfree) class.</jats:p>

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