What does this research mean for the field?

S-submodules generalize S-ideals and exhibit distinct properties, including characterization of modules with only the zero S-submodule and correspondence with primary decomposition. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to define and study S-submodules as a broader concept based on S-ideals, exploring their properties and characterizations.

March 15, 2026Asian-European Journal of Mathematics

On S -submodules of modules over commutative rings

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Authors

AAAdam AnebriUniversité Hassan 1er HKHani A. KhashanAl al-Bayt University

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Implication

Introduces S-submodules in modules over commutative rings, highlighting their properties and implications.

Key Points

The aim is to define and study S-submodules as a broader concept based on S-ideals, exploring their properties and characterizations.
Introduced S-submodules in the context of R-modules and defined their properties.
Characterized modules with only the zero S-submodule.
Examined how primary decomposition relates to S-submodules.
Investigated the impact of S-submodule properties in module constructions such as localization and direct products.
Characterized specific modules based on the existence of S-submodules.
Established that certain submodules correspond to S-submodules when defined by the complement of prime ideals.
Provided examples illustrating the properties and behavior of S-submodules in various contexts.

Cite This Study

Anebri et al. (2026) studied this question.

synapsesocial.com/papers/69b64daeb42794e3e660e465 https://doi.org/10.1142/s1793557126500385

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On S -submodules of modules over commutative rings

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Member takes

Implication

Key Points

Cite This Study

On S -submodules of modules over commutative rings

Discussion

Member takes

Implication

Key Points

Cite This Study

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