On Graded Multiplication-Like Modules

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DOI: https://doi.org/10.28924/2291-8639-24-2026-198
Published: Jul 6, 2026
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Rajáa Al-Qderat, Amani Al-Qderat, Khaldoun Al-Zoubi, On Graded Multiplication-Like Modules, Int. J. Anal. Appl., 24 (2026), 198.

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Rajáa Al-Qderat, Amani Al-Qderat, Khaldoun Al-Zoubi

Abstract

In this article, we introduce the notion of graded multiplication-like modules over commutative graded rings and we obtain some related results. Let \(G\) be a group with identity \(e\). Let \(W=\bigoplus_{g\in G}W_{g}\) be a \(G\)-graded commutative ring and \(D=\bigoplus_{\alpha\in G}D_{\alpha}\) a graded \(W\)-module. We say that \(D\) is a graded multiplication-like if for each graded ideal \(K\) of \(W,\) there exists a graded submodule \(L\) of \(D\) with \(K=(L:_{W}D)\).

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