J. Bartijn, Flatnes, completions, regular sequences un m´enage`a trois, Thesis, Utrecht (1985). L.W. Christensen, Gorenstein dimensions, Lecture Notes in Mathematics, 1747, Springer-Verlag, Berlin (2000). L.W. Christensen and H. Holm, Ascent properties of Auslander categories, Canad. J. Math. , 61(1) (2009) 76-108. L.W. Christensen, A. Frankild and H. Holm, On Gorenstein projective, injective and flat dimensions—a functorial description with applications, J. Algebra, 302(1) (2006) 231-279. E.E. Enoch and O.M.G. Jenda, Relative homological algebra, de Gruyter Expositions in Mathematics, 30, Walter de Gruyter & Co., Berlin (2000). H-B. Foxby, Hyperhomological algebra & commutative rings, in preparation. A. Frankild, Vanishing of local homology, Math. Z., 244 (2003) 615-630. J.P.C. Greenlees and J.P. May, Derived functors of the I-adic completion and local homology, J. Algebra, 149 (1992) 438-453. H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra, 189 (2004) 167-193. J. Lipman, A.J. L´opez and L.A. Tarrio, Local homology and cohomology on schemes, Ann. Sci. Ecole Norm. Sup. , 30(4) (1997) 1-39. E. Matlis, The Koszul complex and duality, Comm. Algebra, 1(2) (1974) 87-144. F. Mohammadi Aghjeh Mashhad and K. Divaani-Aazar, local homology and Gorenstein flat modules, Journal of Algebra and its Applications, 11(2) (2012) 12500221-12500228. T.T. Nam, Generalized local homology modules for artinian modules, Algebra Colloquium, 19(1) (2012) 1205-1212. T.T. Nam, Left derived functors of the generalized I-adic completion and generalized local homology, comm. In Algebra, 38 (2010) 440-453. A-M. Simon, Some homological properties of complete modules, Math. Proc. Cambridge Philos. Soc., 108 (2) (1990) 231-246. S. Yassemi, Generalized section functors, J. Pure Appl. Algebra, 95(1) (1994) 103-119.