On S-2-Prime Hyperideals of Commutative Hyperrings - Tuysuz, Elif; Yesilot, Gursel; Onar, Serkan; Yavuz, Sanem (MDPI, 2026)
This paper introduces the notion of S-2-prime hyperideals, providing a unifying generalization of 2-prime and S-prime hyperideals in multiplicative hyperrings. The key algebraic properties of these hyperideals are explored, and their connections with other classes of hyperideals are investigated. Furthermore, the unique aspects that differentiate S-2-prime hyperideals are emphasized, illustrating their role in expanding the theoretical framework of hyperideal structures. We examine the behavior of these hyperideals under hyperring homomorphisms, extensions, and standard algebraic operations, demonstrating that many established properties of prime, 2-prime, and S-prime hyperideals extend naturally to the S-2-prime setting. Illustrative examples are provided to highlight key distinctions and to offer structural insights. Overall, this work enhances the theoretical understanding of hyperideals in multiplicative hyperrings and establishes a foundational framework for future research.
Keywords: 2-prime hyperideals; S-prime hyperideals; S-2-prime hyperideals; S-PRIME IDEALS; 2-PRIME IDEALS; Mathematics