| Abstract: | If T is a perfect torsion theory for a category of modules over a commutative ring R, a module C is called T—cotorsion provided HomR(QT,C) = 0 = ExtR (QT,C) where QT denotes the T-injective hull of R. Motivated by the now classical results of D. K. Harrison for abelian groups and of E. Matlis for modules over a domain, the theory of T—cotorsion modules is extended. For example, a category equivalence is obtained between the category of T—compact T-cotorsion modules and the category of T-torsion T-reduced modules. The class of T-divisible modules (homomorphic images of T-injective modules) is shown to be closed under formation of extensions if and only if pdRQT ≤ 1, in the case that QT is T—cocritical. |
