TY - JOUR
AU - Jasem, Fatima Dhiyaa
AU - Elewi, Alaa A.
PY - 2022/08/31
Y2 - 2023/06/01
TI - 2-prime submodules of modules
JF - Iraqi Journal of Science
JA - Iraqi Journal of Science
VL - 63
IS - 8
SE - Mathematics
DO - 10.24996/ijs.2022.63.8.34
UR - https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/6409
SP - 3605-3611
AB - <p> 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.</p>
ER -