On primary isolated submodules

Document Type : Research Paper


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


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.