Inverse limit and FP-Injective Hulls of Modules

Abstract:

      Let R be a ring with unit element, and A a left R-module. A is called FP-injective if Ext_R′(P, A)=0 for every finitely presented R-module P. Let E_R(A) denote the injective hull of A. In the paper we prove by means of inverse limit functor that any module A Over coherent ring R has the minimum FP-injective submodule e_R(A) in E_R(A) which contains A and can be defined as the FP-injective hull of A.