General formal local cohomology modules

Abstract

Let (R,m) be a local ring, Ф a system of ideals of R and M a finitely generated R-module. In this paper, we define and study general formal local cohomology modules. We denote the i-th general formal local cohomology module M with respect to Ф by 𝕱ⁱФ(M) and we investigate some finiteness and Artinianness properties of general formal local cohomology modules.