Document Type : Research Paper

Authors

• Ghaleb Ahmed
• Tamara Alshareef

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$\text{ A}⊈C$. Some properties are gained and we look for any relationship between this type of modules and other related modules.

Keywords

• Primary isolated submodules
• Primary lifted submodules
• Primary radical submodules
• Primary submodules
• Prime submodules