REVIEW 1 major objections 7 references
Commutative rings contain a new class of ideals called weakly Q-ideals.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · grok-4.3
2026-06-27 19:02 UTC pith:PXFQLSSQ
load-bearing objection This paper defines weakly Q-ideals and checks some routine properties, but the addition looks too small to matter much. the 1 major comments →
Weakly Q-ideals of commutative rings
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
We introduce and study the notion of weakly Q-ideals in commutative rings.
What carries the argument
The definition of a weakly Q-ideal, a weakened variant of the Q-ideal concept that permits new containment and generation behaviors in commutative rings.
Load-bearing premise
The chosen definition of weakly Q-ideal produces non-trivial properties or relations worth proving in the theory of commutative rings.
What would settle it
A concrete check would be to verify whether every weakly Q-ideal satisfies only the same properties already known for Q-ideals or other named ideal classes with no additional relations or examples.
If this is right
- Weakly Q-ideals admit characterizations in terms of their generators and annihilators within the ring.
- The notion interacts with standard operations such as sums, products, and radicals of ideals.
- Specific commutative rings, including domains and local rings, furnish examples where weakly Q-ideals appear distinctly.
Where Pith is reading between the lines
- The definition may connect to other weakened ideal notions already studied in commutative algebra, such as weakly prime ideals.
- Further work could test whether weakly Q-ideals correspond to geometric objects in the spectrum of the ring.
- Applications might appear in homological algebra when tracking how these ideals behave under localization.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript introduces the notion of weakly Q-ideals in commutative rings and studies associated properties.
Significance. The introduction of a new class of ideals could contribute to the theory of commutative rings if it yields non-trivial characterizations, relations to existing ideal types (such as prime or primary ideals), or applications; however, the provided abstract gives no indication of specific theorems, examples, or connections that would establish broader impact.
major comments (1)
- The manuscript consists solely of the abstract statement with no definitions, theorems, proofs, examples, or sections provided for examination; this prevents verification of whether the introduced notion produces non-trivial results as assumed in the weakest assumption.
Simulated Author's Rebuttal
We thank the referee for their report. The major comment is addressed point-by-point below.
read point-by-point responses
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Referee: The manuscript consists solely of the abstract statement with no definitions, theorems, proofs, examples, or sections provided for examination; this prevents verification of whether the introduced notion produces non-trivial results as assumed in the weakest assumption.
Authors: We acknowledge that the text supplied in the current query consists only of the abstract sentence. If the version sent to the referee was likewise truncated, this constitutes a submission error. The complete manuscript defines weakly Q-ideals, establishes their basic properties, provides characterizations relative to prime and primary ideals, includes concrete examples in specific rings, and contains proofs of the stated results. The revised submission will contain the full text with all sections, definitions, theorems, and examples. revision: yes
Circularity Check
No significant circularity
full rationale
The paper consists solely of the introduction and study of a newly defined notion (weakly Q-ideals) in commutative rings. No equations, fitted parameters, predictions, or load-bearing self-citations appear in the abstract or described content. The central claim reduces only to the act of defining the term and deriving associated properties from that definition, which is self-contained and does not reduce any result to its own inputs by construction. This matches the default expectation for definitional papers in algebra with no detectable circular steps.
Axiom & Free-Parameter Ledger
read the original abstract
In this paper, we introduce and study the notion of weakly Q-ideals in commutative rings.
Reference graph
Works this paper leans on
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[1]
D. D. Anderson, E. Smith,Weakly prime ideals,Houston J. Math.,29(4) (2003) 831–840
2003
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[2]
Anderson, M.Winders, Idealization of a Module, Journal of Commutative Algebra, 1(1) (2009) 3-56
D.D. Anderson, M.Winders, Idealization of a Module, Journal of Commutative Algebra, 1(1) (2009) 3-56
2009
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[3]
S. E. Atani, F. Farzalipour,On weakly primary ideals, Georgian Mathematical Journal,12(3) (2005) 423-429
2005
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[4]
Ersoy, S
B.A. Ersoy, S. Ko¸ c,¨U. Tekır, G. Yesilot, E. Yildiz,On weakly(1, n)-ideals and weaklyn-ideals, Czech. Math. J.,75(2025) 611–628
2025
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[5]
Khashan, E.Y
H.A. Khashan, E.Y. Celikel,WeaklyJ-ideals of commutative rings,36(2) (2022) 485-495
2022
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[6]
Mimouni,Nil-ideals,J-ideals and their generalizations in commutative rings,Beitr
A. Mimouni,Nil-ideals,J-ideals and their generalizations in commutative rings,Beitr. Al- gebra Geom., (2022). https://doi.org/10.1007/s13366-022-00668-6
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[7]
Smach,S-Q-ideals and almostS-Q-ideals of commutative rings,Commun
S. Smach,S-Q-ideals and almostS-Q-ideals of commutative rings,Commun. Korean Math. Soc.,40(4) (2025) 753-761. Department of Mathematics, F aculty of Sciences, Imam Khomeini International Uni- versity, Qazvin, Iran. Email address:m.anbarloei@sci.ikiu.ac.ir
2025
discussion (0)
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