What does this research mean for the field?

Modules satisfying condition (*) have structural properties that allow the direct sum of two such modules to inherit this condition under certain circumstances. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The study aims to understand R-modules where every quasi-primary submodule is also primary, and explore the implications for prime ideals.

February 17, 2026Open Access

On sM-Prime Ideals in Commutative Rings

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Authors

GUGülşen UlucakGebze Technical University VLVioleta Leoreanu-FoteaAlexandru Ioan Cuza University SGSeçil Çeken GüneşTrakya University

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Implication

Investigates weak sM-prime ideals in R-modules, revealing structural properties and interactions between modules and rings.

Key Points

The study aims to understand R-modules where every quasi-primary submodule is also primary, and explore the implications for prime ideals.
Analyzed commutative rings and unital modules
Examined structural properties of modules satisfying condition (*)
Investigated direct sums of modules M1 and M2
Defined weak sM-prime ideals relative to R-modules
Identified conditions under which a direct sum inherits condition (*)
Characterized when P-quasi-primary submodules are P-primary
Developed a framework connecting quasi-primary structures with prime ideals

Cite This Study

Ulucak et al. (2026) studied this question.

synapsesocial.com/papers/6994055d4e9c9e835dfd6487 https://doi.org/10.3390/axioms15020142

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On sM-Prime Ideals in Commutative Rings

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Member takes

Implication

Key Points

Cite This Study

On sM-Prime Ideals in Commutative Rings

Discussion

Member takes

Implication

Key Points

Cite This Study

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