International Journal of Neutrosophic Science
IJNS
2690-6805
2692-6148
10.54216/IJNS
https://www.americaspg.com/journals/show/4058
2020
2020
On Graded S-semiprime Submodules of Graded Modules Over Graded Commutative Rings
Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O.Box 3030, Irbid 22110, Jordan
Khaldoun
Khaldoun
Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O.Box 3030, Irbid 22110, Jordan
Khaldoun Al
Al-Zoubi
Let G be a group with identity e. Let T be a commutative G-graded ring with non-zero identity, W be a graded T-module and S ⊆ h(T) a multiplicatively closed subset of T. In this article, we introduce and study the concept of graded S-semiprime submodules. A graded submodule K of W with (K :T W) ∩ S = ∅ is said to be graded S-semiprime, if there exists a fixed st ∈ S such that whenever rn i mj ∈ K for some ri ∈ h(T), mj ∈ h(W), t, i, j ∈ G, and n ∈ N, then strimj ∈ K. Some characterizations and properties of graded S-semiprime submodules are given.
2026
2026
188
194
10.54216/IJNS.270216
https://www.americaspg.com/articleinfo/21/show/4058