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September 30, 2025Open Access

S-Ideals: A Unified Framework for Ideal Structures via Multiplicatively Closed Subsets

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The concept of S-ideals generalizes various classical ideals, enhancing the understanding of their structure.
For instance, r-ideals emerge from regular elements, while S-ideals coincide with primary ideals defined by prime ideals.
This work reveals connections between S-ideals and von Neumann regularity in localization processes.
The exploration encompasses polynomial rings and amalgamated constructions based on diverse choices of S.

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Analysis of S-ideals shows structural properties in commutative rings, highlighting their behavior in polynomial rings and idealizations.

Khashan et al. (2025) studied this question.

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