On (2, n)-Hyperideals of Commutative Multiplicative Hyperrings

We introduce and study (2, n)-hyperideals in commutative multiplicative hyperrings, a new class of hyperideals that simultaneously generalizes n-hyperideals and 2-absorbing primary hyperideals. Our central result characterizes (2, n)-hyperideals intrinsically: a proper hyperideal I is a (2, n)-hyperideal if and only if it is 2-absorbing primary and √I = √0. As a consequence, a hyperring R admits a (2, n)-hyperideal precisely when R has at most two minimal prime hyperideals—provided all hyperideals are C-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 (2, n)- 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.