On graded 1-absorbing \(\delta\)-primary ideals
type: Item
instance of: scholarly article
title: On graded 1-absorbing \(\delta\)-primary ideals
zbMATH Open document ID: 1546.13003
author: Rashid Abu-Dawwas
author: Anass Assarrar
author: Jebrel M. Habeb
author: Najib Mahdou
published in: Proyecciones
publication date: 2024-08-13T00:00:00Z
review text: This paper introduces and studies the concept of graded 1-absorbing \(\delta\)-primary ideals in commutative graded rings. By extending the notion of 1-absorbing \(\delta\)-primary ideals to graded rings, the authors explore how this new class of ideals interacts with other established classes, such as graded \(\delta\)-primary ideals and graded 1-absorbing prime ideals. The paper further examines the behavior of graded 1-absorbing \(\delta\)-primary ideals in localized graded rings and graded idealization, offering several key results and illustrative examples.\N\NThe paper provides a valuable contribution by expanding the theory of graded rings through the introduction of graded 1-absorbing \(\delta\)-primary ideals. This new class builds upon existing structures in ideal theory and opens up new avenues for research in the algebraic properties of graded rings. Notably, the results in Theorem 2.7 and Proposition 2.4 establish important connections between graded 1-absorbing \(\delta\)-primary ideals and other well-known classes of ideals, offering insights that are both theoretically interesting and potentially impactful for future studies.\N\NThe paper is generally well-organized and presents its definitions, lemmas, and theorems in a logical and coherent manner. The use of examples, such as Example 2.3, helps to clarify the introduced concepts, though the addition of further examples in some sections could enhance the clarity of the more abstract results. The writing is clear, although certain proofs, particularly those in Theorem 2.7 and Proposition 2.4, might benefit from additional explanation to make the reasoning more accessible to a wider audience.\N\NWhile the paper offers a strong contribution, a few areas could be enhanced:\N\begin{itemize}\N\item \textbf{Additional Examples:} Including more examples, particularly in Sections 3 and 4, would help to further illustrate the practical implications of the theoretical results.\N\item \textbf{Clarification in P…
reviewed by: Shadi Shaqaqha
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 13C13
zbMATH DE Number: 7896265
zbMATH Keywords: graded rings
zbMATH Keywords: 1-absorbing ideals
zbMATH Keywords: \(\delta\)-primary ideals
zbMATH Keywords: graded \(\delta\)-primary ideals
zbMATH Keywords: graded algebra
zbMATH Keywords: trivial ring extensions
zbMATH Keywords: localization of graded rings
MaRDI profile type: Publication
cites work: Q5053387
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DOI: 10.22199/ISSN.0717-6279-6190
description: scientific article; zbMATH DE number 7896265