What does this research mean for the field?

The notion of S-1-absorbing primary submodules extends 1-absorbing primary submodules, possessing distinct algebraic properties and satisfying specific avoidance, idealization, and amalgamation theorems. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To introduce and characterize the concept of S-1-absorbing primary submodules as an extension of classical 1-absorbing primary submodules in commutative ring theory.

August 30, 2026Czechoslovak Mathematical JournalOpen Access

On S-1-absorbing primary submodules

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Authors

MIMohammed IssoualSidi Mohamed Ben Abdellah University NMNajib MahdouSidi Mohamed Ben Abdellah University EÇEce Yetki̇n Çeli̇kelHasan Kalyoncu University

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Implication

Algebraic analysis characterizes S-1-absorbing primary submodules across rings and modules, demonstrating key algebraic properties including avoidance, idealization, and amalgamation.

Key Points

To introduce and characterize the concept of S-1-absorbing primary submodules as an extension of classical 1-absorbing primary submodules in commutative ring theory.
Defined S-1-absorbing primary submodules relative to a multiplicatively closed subset S of a commutative ring R and an R-module M.
Evaluated structural behaviors and algebraic preservation using ring idealization and amalgamation constructions.
Derived foundational algebraic characterizations and structural criteria for S-1-absorbing primary submodules.
Formulated and proved an S-1-absorbing primary avoidance theorem.
Established necessary and sufficient conditions for the preservation of the S-1-absorbing primary property under idealization and amalgamation.

Cite This Study

Issoual et al. (2026) studied this question.

synapsesocial.com/papers/6a93efc06c1a8fb52e79bc86 https://doi.org/10.21136/cmj.2026.0030-26

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Implication

Algebraic analysis characterizes S-1-absorbing primary submodules across rings and modules, demonstrating key algebraic properties including avoidance, idealization, and amalgamation.

On S-1-absorbing primary submodules

Discussion

Member takes

Implication

Key Points

Cite This Study

On S-1-absorbing primary submodules

Discussion

Member takes

Implication

Key Points

Cite This Study

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