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