# 2-irreducible and strongly 2-irreducible submodules of a module

## TL;DR

This paper introduces and explores the properties of 2-irreducible and strongly 2-irreducible submodules in modules over commutative rings, generalizing existing concepts of irreducibility.

## Contribution

It defines new classes of submodules, 2-irreducible and strongly 2-irreducible, and investigates their properties as a generalization of irreducible submodules.

## Key findings

- Defined 2-irreducible and strongly 2-irreducible submodules.
- Analyzed properties and relationships of these submodules.
- Extended the theory of submodules in module theory.

## Abstract

Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2- irreducible) submodules of M as a generalization of irreducible (resp., strongly irreducible) submodules of M and investigated some properties of these classes of modules.