Essential-small fully stable modules

Document Type : Research Paper


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


We will add new types of modules over a ring $\mathfrak{R}$ called $\mathit{g}-$ small completely stable module and $\mathit{g}-$ small duo module, assuming $\mathfrak{R}$ is a ring with identity and $\mathcal{M}$ is a unitary left $\mathfrak{R}$-module. We also present the $\mathit{g}-$ small dual stable module, which is a duality. We show that our new ideas have characterization and a few properties.