# 2-prime submodules of modules

## Authors

• Fatima Dhiyaa Jasem Department of mathematics, College of Science, University of Baghdad, Baghdad, Iraq
• Alaa A. Elewi Department of mathematics, College of Science, University of Baghdad, Baghdad, Iraq

## Keywords:

prime ideal, prime submodules, 2-prime ideal, primary submodule

## Abstract

Let R be a commutative ring with unity. And let E be a unitary R-module. This paper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that  or . we prove many properties for this kind of submodules, Let H is a submodule of module F over a ring R then H is a 2-prime submodule if and only if [N ] is a 2-prime submodule of E, where r R. Also, we prove that if F is a non-zero multiplication module, then [K: F] [H: F] for every submodule k of F such that H K. Furthermore, we will study the basic properties of this kind of submodules.

2022-08-31

## How to Cite

Jasem, F. D. ., & Elewi, A. A. (2022). 2-prime submodules of modules. Iraqi Journal of Science, 63(8), 3605–3611. https://doi.org/10.24996/ijs.2022.63.8.34

Mathematics