On S-2 Prime Hyperideals of Commutative Hyperrings

In this paper, we present the notion of S-2-prime hyperideals, which provides a unifying generalization of 2-prime and S-prime hyperideals within multiplicative hyperrings. We explore their key algebraic properties and investigate their connections with other hyperideal classes. We emphasize the unique aspects that differentiate S-2-prime hyperideals, illustrating their role in expanding the theoretical framework of hyperideal structures. We examine how these hyperideals behave under hyperring homomorphisms, extensions, and standard algebraic operations, demonstrating that many known properties of prime, 2-prime, and S-prime hyperideals extend naturally to the S-2-prime setting. We provide illustrative examples to highlight important differences and to offer practical insight into their structure. Overall, we enhance the theoretical understanding of hyperideals in multiplicative hyperrings and establish a framework for future research in this area.