Derived Functors of the Torsion Functor and Local Cohomology of Noncommutative Rings

Let R be an associative ring which is not necessarily commutative. For any torsion theory T on the category of left R-modules and for any nonnegative integer n we define and study the notion of the n th local cohomology functor with respect to T. For suitably nice rings a bound for the nonvanishing of these functors is given in terms of the T-dimension of the modules. 1980 Mathematics subject classification (Amer. Math. Soc.): primary 16A08, 16A63, 18E25, 18G10; secondary 13D03, 16A55, 18E40.