H-essential submodules and Homessential modules

الملخص EN

The main goal of this paper is introducing and studying a new concept, which is named H-essential submodules, and we use it to construct another concept called Homessential modules.

Several fundamental properties of these concepts are investigated, and other characterizations for each one of them is given.

Moreover, many relationships of Homessential modules with other related concepts are studied such as Quasi-Dedekind, Uniform, Prime and Extending modules.