Square-Difference Factor Absorbing Primary Hyperideals of Multiplicative Hyperrings

We introduce and study square-difference factor absorbing primary hyperideals (sdf-absorbing primary hyperideals) in commutative multiplicative hyperrings. A proper hyperideal I is called sdf-absorbing primary if x2−y2⊆I implies x+y∈I or x−y∈I. This class provides a proper common generalization of both primary hyperideals and sdf-absorbing hyperideals. We establish a comprehensive characterization; investigate the behavior under homomorphisms, localization, intersections, ascending chains, and Cartesian products; and identify the precise conditions under which the three notions coincide.