2-Prime Modules

Fatima Dhiyaa Jasem; Alaa A. Elewi

doi:10.24996/ijs.2023.64.5.26

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

DOI:

https://doi.org/10.24996/ijs.2023.64.5.26

Keywords:

prime ideal, 2-prime ideal, prime module, 2-prime module, primary module

Abstract

In this paper, we introduce the notion of a 2-prime module as a generalization of prime module E over a ring R, where E is said to be prime module if (0) is a prime submodule. We introduced the concept of the 2-prime R-module. Module E is said to be 2-prime if (0) is 2-prime submodule of E. where a proper submodule K of module E is 2-prime submodule if, whenever rR, xE, E, Thus xK or [K: E].