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

We introduce and study [Formula: see text]-hyperideals in commutative multiplicative hyperrings, a new class of hyperideals that simultaneously generalizes [Formula: see text]-hyperideals and 2-absorbing primary hyperideals. Our central result characterizes [Formula: see text]-hyperideals intrinsically: a proper hyperideal [Formula: see text] is a [Formula: see text]-hyperideal if and only if it is 2-absorbing primary and [Formula: see text] = [Formula: see text]. As a consequence, a hyperring [Formula: see text] admits a [Formula: see text]-hyperideal precisely when [Formula: see text] has at most two minimal prime hyperideals—provided all hyperideals are [Formula: see text]-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: see text]-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.