@article{Prakash2025,
title = {ISO $C2$ and  ISO $C3$-Modules},
author = {Surya Prakash, Ajim Uddin Ansari,Anurag Shukla},
journal = {Indian Journal of Mathematics},
volume = {67},
number = {1},
year = {2025},
pages = {71--75},
issn = {0019-5324},
keywords = {Isosimple modules; direct injective modules; iso $C2$-modules; iso $C3$-modules.},
abstract = {In this paper, we introduce and study the concept of iso $C2$-modules and iso $C3$-modules as generalizations of the direct injective modules.  We prove that $M$ is an iso $C3$-module if for any two isosimple submodules $A, B$ of $M$ with $A\cong B, B\subseteq ^\oplus M$ and $A\cap B = 0$ implies that $A\subseteq ^ \oplus M$. Also, if $M$ is an iso $C3$- module then  $Im f\subseteq ^\oplus B$, whenever $M = A\oplus B$ with $A, B$ isosimple and $f: A\rightarrow B$ be an $R$-homomorphism. Furthermore, we provide a number of properties and characterizations of these new classes of modules.}
}