On Graded Weakly S-2-Prime Ideals

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DOI: https://doi.org/10.28924/2291-8639-24-2026-264
Published: Aug 24, 2026
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Reem Abu Zuraiq, Khaldoun Al-Zoubi, On Graded Weakly S-2-Prime Ideals, Int. J. Anal. Appl., 24 (2026), 264.

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Reem Abu Zuraiq, Khaldoun Al-Zoubi

Abstract

Let \(G\) be a group with identity \(e\), let \(\mathfrak{T}\) be a commutative \(G\)-graded ring, and let \(S\subseteq h(\mathfrak{T})\) be a multiplicatively closed subset of \(\mathfrak{T}\). In this paper, we introduce and study graded weakly \(S\)-2-prime ideals, which extend the notion of graded weakly \(2\)-prime ideals in graded commutative rings. We establish several basic properties and characterizations of these ideals and investigate their relationship with graded \(S\)-2-prime ideals. In particular, we examine the role of graded \(S\)-double-zeros and obtain conditions under which graded weakly \(S\)-2-prime ideals coincide with graded \(S\)-2-prime ideals. We further study these ideals in graded idealizations and amalgamated algebras. Several examples are included to illustrate the main concepts and results.

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