$H-\mu^{\ast}_e$-essential-supplemented modules

Document Type : Research Paper


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


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.


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Volume 13, Issue 2
July 2022
Pages 1447-1453
  • Receive Date: 10 January 2022
  • Revise Date: 22 February 2022
  • Accept Date: 17 March 2022