On quasi-\(n\)-ideals of commutative rings (Q6601863)

The authors of this paper introduced and studied a new class of ideals in commutative algebra called quasi-\(n\)-ideals, which generalize \(n\)-ideals by focusing on their relationship with the nil-radical of a ring. Quasi-\(n\)-ideals are shown to exist only if the nil-radical is prime. The authors also characterized rings where the nil-radical is either a maximal or minimal ideal. They also explore how these ideals behave in ring extensions, such as quotient rings, localization of a ring, polynomial ring, and trivial ring extension, and they provide several examples to illustrate their distinct properties. The paper contributes to a deeper understanding of ideal structures in commutative rings, especially in the context of strongly quasi-primary ideals and their generalizations.