Some Results on Quasi-Semiprime Submodules

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 ,...

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Bibliographic Details
Published in:Journal of physics. Conference series 2021-03, Vol.1818 (1), p.12189
Main Authors: Al-Ragab, Omar M., Al-Mothafar, Nuhad S.
Format: Article
Language:English
Subjects:
Modules
Physics
Rings (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1818/1/012189