A Study of Some Generalizations of Local Homology

Tate local cohomology and Gorenstein theory, which are important generalizations of the classical cohomology, has been investigated. It found that they have such vanishing properties long exact sequences. However, for homology, what about duality? In this paper we concerned with homology homology. first part generalize as study properties, artinianness some sequence modules. We find an artianian R-module M a finitely generated N finite projective dimension, module respect to ideal I is also artinian module. second consider modules version. discuss sequences obtain connecting Gorenstein, generalized Finally, applicaton these modules, R-modules dimension admitting proper resolution respectively, coincides in certain cases.