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

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

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In this study, here 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 flexcon reverse osmosis water storage tank are soft prime int-ideals.Lastly, we examined soft homomorphic images and preimages of these new structures.