Volume 27 • Issue 2 • PP: 188-194 • 2026
On Graded S-semiprime Submodules of Graded Modules Over Graded Commutative Rings
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© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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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.
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References
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