### On primary isolated submodules

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Pure Science, Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq

Abstract

Let $L$ be a left module over a ring $\text{\ S}$ with identity. In this paper, the concept of primary isolated submodules is introduced. We look for relations between this class of submodules and related modules. A number of facts and characterizations that concern is gained. The aim of this work is to introduce and study the primary isolated submodules as a generalization of isolated submodules. A submodule $A$ of $L$ is primary isolated if for each proper $B$ of $A$, there is a primary submodule $C$ of $L$, $B \subseteq C$ but$\text{\ A} \nsubseteq C$. Some properties are gained and we look for any relationship between this type of modules and other related modules.

Keywords