Local Cohomology Without Direct Limits and Local Homology Without Inverse Limits

Abstract

In this dissertation, we study the computation of local cohomology and local homology of R-modules without using direct limits and inverse limits respectively. We construct subcategories, C of R-Mod such that the I-torsion functor ΓI (−) is isomorphic to a single left exact additive functor F(−). This simplifies the computation of local cohomology module with respect to the ideal I of R. On the other hand, we construct subcategories, D of R-Mod such that the I-adic completion functor ΛI (−) is isomorphic to a single right exact additive functor G(−). This simplifies the computation of local homology modules with respect to the ideal I of R