SOME d -TRANSFORM FUNCTORS BASED ON AN IDEAL

Let R be a commutative Noetherian ring, b be an ideal of R, M an R-module and let d be a non-negative integer.We introduce a general d-transform functor T d,b (M, ) and its right derived functors T i d,b (M, ), i ∈ N0, on the category of R-modules and study their various properties.The connection of these functors with some kind of generalized local cohomology functors H i d,b (M, ) is discussed.When both M and N are finitely generated, some finiteness results on T i d,b (M, N ) and H i d,b (M, N ) are concluded.Then, we study how the depth and dimension of certain subsets of Spec(R) affect the behavior and vanishing of these modules.