Open AccessSome Results on Quasi-Semiprime Submodules
Author(s) -
Omar M Al-Ragab,
Nuhad S. Al-Mothafar
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1818/1/012189
Subject(s) - semiprime , semiprime ring , mathematics , ideal (ethics) , commutative property , pure mathematics , combinatorics , philosophy , prime (order theory) , epistemology
Let R be a commutative ring with unity and let B be a submodule of a non-zero left R-module D , B is called semiprime if whenever a k y ∈ B , a ∈ R , y ∈ D , k ∈ Z + implies a y ∈ B . We say that a proper submodule B of an R-module D is a quasi-semiprime submodule if whenever a k b y ∈ B , where a , b ∈ R , y ∈ D , k ∈ Z + implies that a b y ∈ B . Equivalently, a proper submodule B of an R-module D is said to be a quasi-semiprime submodule if and only if [ B ∶ ( y )] is a semiprime ideal of R for each y ∈ D . We give many results of this type of submodules.