Cofinitely essential g-supplemented modules

Let M be an R-module. If every cofinite essential submodule of M has a g-supplement in M, then M is called a cofinitely essential g-supplemented (or briefly cofinitely eg-supple-mented) module. In this work, some properties of these modules are investigated. It is proved that every factor module and every homomorphic image of a cofinitely eg-supplemented module are cofinitely eg-supplemented. Let M be a cofinitely eg-supplemented module. Then every M-generated R-module is cofinitely eg-supplemented.