(2,n)-hyperidealn-hyperideal C-idealKrull dimension Von Neumann regular hyperring On (2,n)-hyperideals of commutative multiplicative hyperrings
Journal of Algebra and its Applications, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1142/s0219498828500272
- Dergi Adı: Journal of Algebra and its Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: hyperideal, Multiplicative hyperring
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
In this paper, we introduce and study (Formula presented)-hyperideals in commutative multiplicative hyperrings, a new class of hyperideals that simultaneously generalizes (Formula presented)-hyperideals and 2-absorbing primary hyperideals. Our central result characterizes (Formula presented)-hyperideals intrinsically: a proper hyperideal (Formula presented) is a (Formula presented)-hyperideal if and only if it is 2-absorbing primary and (Formula presented). As a consequence, a hyperring (Formula presented) admits a (Formula presented)-hyperideal precisely when (Formula presented) has at most two minimal prime hyperideals provided all hyperideals are (Formula presented)-ideals, a condition that has no classical analogue and underscores a fundamental departure from ordinary ring theory. We establish a complete hierarchy among the main classes of hyperideals, prove stability under radicals and finite intersections, and characterize those hyperrings in which every proper hyperideal is a (Formula presented)-hyperideal. We further connect this theory to Krull dimension, Von Neumann regularity, and the structure of quotient hyperfields. Throughout, explicit counterexamples demonstrate where classical ideal-theoretic arguments break down in the multivalued setting, revealing the genuine novelty of the hyperstructure framework.