Cofinitely Injective and Projective Modules

Abstract

In this work, cofinitely injective and cofinitely projective modules are defined. Some properties of cofinitely injective and cofinitely projective modules are investigated. Let N be an R-module. Then every R-module is cofinitely N-injective if and only if every cofinite submodule of N is a direct summand. This is also true for cofinitely projective modules. Let M be a nonzero R-module. If every cofinitely M-projective (M-injective) module is M-projective (M-injective) then Rad M ≠ M.