Cousin Complexes and Almost Flat Rings

Let (Rm) be a d-dimensional Noetherian local ring and T be a commutative strict algebra with unit element lt over R such that mT + T. We define almost exact sequences of T-modules and characterize almost flat T-modules. Moreover, we define almost (faithfully) flat homomorphisms between R-algebras T and W, where W has similar properties that I has as an R-algebra. By almost (faithfully) flat homomorphisms and almost flat modules, we investigate Cousin complexes of T and W-modules. Finally, for a finite filtration F = (F)0 of length less than d of Spec(T) such that it admits a T-module X, we show that 'E. := Torm (M, H4-4 (CT (F, X))) ? Hp+a(Tot(7)) and TIE, := Hd-P (Tora (M,CT (F, X))) Hp+a (Tot(T)), where M is an any flat T-module and as a result we show that E, and "E, are almost zero, when M is almost flat.