On Soft Near-Prime Int-Ideals and Soft 1-Absorbing Prime Int-Ideals With Applications

İbrahim Halil Kanat and Filiz Çıtak

Journal of Mathematics, 2025, vol. 2025, 1-12

Abstract: In this study, we aimed to introduce two different generalizations of the soft prime int-ideal and clarify the relationships between the soft prime int-ideal and the substructures of a ring. First, we explored new algebraic features of the soft prime int-ideal. We defined and exemplified essential concepts such as soft nilpotent elements, soft idempotent elements, nonexplicit soft int-ideals, one-to-one soft sets, and soft zero divisors of a soft int-ideal. Then, we investigated the behavior of soft nilpotent and soft idempotent elements in relation to the soft prime int-ideal. We then defined a soft near-prime int-ideal, which is a generalization of the soft prime int-ideal through soft radicals, and examined its properties. Furthermore, we analyzed the relationships between the soft prime int-ideal and the soft near-prime int-ideal, showing that every soft prime int-ideal is a soft near-prime int-ideal, but the converse does not hold. In addition, we proposed the concept of a soft 1-absorbing prime int-ideal as another generalization of the soft prime int-ideal and studied its basic properties. We proved that the radicals of soft near-prime int-ideals and soft 1-absorbing prime int-ideals are soft prime int-ideals. Lastly, we examined soft homomorphic images and preimages of these new structures.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1548808

DOI: 10.1155/jom/1548808

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