d-Transform Functor and Some Finiteness and Isomorphism Results

Abstract

Let R be a Noetherian ring, M be an R-module and let d be a non-negative integer. We introduce the R-module U d(M) and the functor T d(-) on the category of R-modules. General concerning results on the module T d(M) and its relationship with d-local cohomology modules Hid will be given. Then, whenever M is finitely generated, under a mild condition we show that T d(M)≅U d(M), which turns out a result on the finiteness of the set AssR(Td(M)). Finally a criterion for the isomorphism M≅U d(M) will be given. © 2013 Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.