What question did this study set out to answer?

The aim is to characterize S-Jacobson radical submodules and explore their properties and relations in module theory.

On the Characterization and Properties of S -Jacobson radical Submodules

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Introduces S-Jacobson radical submodules, revealing their structure and relationships in algebraic settings.

The aim is to characterize S-Jacobson radical submodules and explore their properties and relations in module theory.
Introduced J S (M) as the set of S-non-generators for modules over a commutative ring.
Examined how J S (M) behaves under module homomorphisms and its relationships with other radical notions.
Provided examples to differentiate S-Jacobson radicals from classical Jacobson radicals.
Established natural inclusion theorems for the S-Jacobson radical and related radicals.
Identified sufficient conditions for equality among the S-Jacobson radical, S-radical, and classical Jacobson radical.
Presented an S-version of Nakayama's lemma applicable to S-finitely generated modules.

Abouhalaka et al. (2026) studied this question.

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