What question did this study set out to answer?

To introduce S-primary ideals relative to a multiplicative subset in commutative rings with identity and investigate their structural properties across various ring constructions.

September 21, 2021Communications in Algebra

S-primary ideals of a commutative ring

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Authors

EMEssebti MassaoudUniversity of Gafsa

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Implication

Theoretical study reveals the structure and properties of S-primary ideals in commutative ring constructions, indicating how classical primary ideal theory extends under multiplicative subsets.

Key Points

To introduce S-primary ideals relative to a multiplicative subset in commutative rings with identity and investigate their structural properties across various ring constructions.
Defined an S-primary ideal P disjoint from multiplicative subset S via the condition that ab in P implies sa in P or sb in P for a fixed s in S.
Evaluated algebraic behaviors in ring amalgamations along an ideal J, trivial ring extensions, and bi-amalgamations.
Established that S-primary ideals reproduce key algebraic properties of classical primary ideals in commutative ring settings.
Characterized the explicit configurations of S-primary ideals within trivial ring extensions and bi-amalgamated ring structures.

Cite This Study

Essebti Massaoud (2021) studied this question.

synapsesocial.com/papers/69db0f7f1e19c8ae088360d8 https://doi.org/10.1080/00927872.2021.1977939

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Implication

Theoretical study reveals the structure and properties of S-primary ideals in commutative ring constructions, indicating how classical primary ideal theory extends under multiplicative subsets.

S-primary ideals of a commutative ring

Discussion

Member takes

Implication

Key Points

Cite This Study

S-primary ideals of a commutative ring

Discussion

Member takes

Implication

Key Points

Cite This Study

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