Volume 27 , Issue 2 , PP: 188-194, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Mohammad Alkhatib 1 , Khaldoun Al-Zoubi 2 *
Doi: https://doi.org/10.54216/IJNS.270216
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.
Graded S-semiprime submodule , Graded S-semiprime ideal , Graded semiprime submodule
[1] K. Al-Zoubi, R. Abu-Dawwas and I. Al-Ayyoub, Graded semiprime submodules and graded semi-radical of graded submodules in graded modules, Ricerche mat., 66 (2) (2017), 449–455.
[2] K. Al-Zoubi and S. Alghueiri, On graded Jgr -semiprime submodules, Italian Journal of Pure and Applied Mathematics, 46 (2021), 361–369.
[3] S.E. Atani, On Graded Prime Submodules, Chiang Mai J. Sci. 33 (1) (2006), 3–7.
[4] J. Escoriza and B. Torrecillas, Multiplication Objects in Commutative Grothendieck Categories, Comm. in Algebra, 26 (6) (1998), 1867-1883.
[5] F. Farzalipour and P. Ghiasvand, On Graded Semiprime and Graded Weakly Semiprime Ideals, Int. Electron. J. Algebra 13 (2013), 15–22.
[6] J. Smith and A. Johnson, Graded Semiprime Ideals in Non-Commutative Rings, Journal of Algebra and Its Applications 23 (4) (2023), 123–135.
[7] P. Ghiasvand, P. and F. Farzalipour, Graded Semiprime Submodules Over non–Commutative Graded Rings. Journal of Algebraic Systems, 10 (1) (2022), 95-110.
[8] R. Hazrat, Graded Rings and Graded Grothendieck Groups, Cambridge University Press, Cambridge, 2016.
[9] S.C Lee, R. Varmazyar, Semiprime submodules of Graded multiplication modules, J. Korean Math. Soc. 49(2) (2012), 435-447.
[10] C. Nastasescu, F. Van Oystaeyen, Graded and filtered rings and modules, Lecture notes in mathematics 758, Berlin-New York: Springer-Verlag, 1982.
[11] C. Nastasescu, F. Van Oystaeyen, Graded Ring Theory, Mathematical Library 28, North Holand, Amsterdam, 1982
[12] Nastasescu, F. Van Oystaeyen, Methods of Graded Rings, LNM 1836. Berlin-Heidelberg: Springer- Verlag, 2004.
[13] H. A.Tavallaee and M. Zolfaghari, Graded weakly semiprime submodules of graded multiplication modules, Lobachevskii J. Math. 34 (1) (2013), 61–67.
