ISO $C2$ and  ISO $C3$-Modules

Prakash, Surya; Ansari, Ajim Uddin; Shukla, Anurag

Indian Journal of Mathematics

ISO $C2$ and ISO $C3$-Modules

Author(s): Surya Prakash Surya Prakash Department of Mathematics,
CMP Degree College, University of Allahabad,
Prayagraj-211002,
India. suryaprakash.maths@gmail.com , Ajim Uddin Ansari Ajim Uddin Ansari Department of Mathematics,
CMP Degree College, University of Allahabad,
Prayagraj-211002,
India. ajimmatau@gmail.com , Anurag Shukla Anurag Shukla Department of Mathematics,
CMP Degree College, University of Allahabad,
Prayagraj-211002,
India. ashukla.math@gmail.com

Vol. 67, No. 1 (2025) • pp. 61–75

Published 27-04-2026 Article History Received 01-10-2025 Revised 19-01-2026 Published 27-04-2026

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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.

Keywords

Isosimple modules; direct injective modules; iso $C2$-modules; iso $C3$-modules.

2020 Mathematics Subject Classification

16D50, 16D60, 16D70.

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Allahabad Mathematical Society

ISO $C2$ and ISO $C3$-Modules

Abstract

Keywords

2020 Mathematics Subject Classification

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