Document Type : Research Paper

Authors

• Adnan Saleh Wadi
• Wasan Khalid Hasan

Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq

Abstract

Let $R$ be a ring  and  $M$ be a unital left $R$-module. We define $\mu^{\ast}$-essential extension relation on the set of submodules of $M$ and investigate its properties. Moreover, we define $H$-$\mu^{\ast}$-essential-supplemented on $M$ and investigate the relations between $M$ and direct summand of its submodules.

Keywords

• $mu^{ast}$-essential–relation
• $H-mu^{ast}$-essential–supplemented
• completely $H-mu^{ast}$-essential–supplemented
• $mu^{ast}$ co–essential submodule
• $mu^{ast}$ co–closed submodule