Pure Essential-Coessential and Pure Essential-Coclosed Submodules

During this work, we introduce concepts named pure-essential coessential sub-modules and pure- essential coclosed submodules. Various properties related with these concepts are considered. Let , be sub-modules of an -module in which case , subsequently is called pure essential-coessential sub-module of , if , and is said to be pure essential-coclosed sub-module, if implies that .