n−absorbing i−prime hyperideals in multiplicative hyperrings

In this paper, we define the concept i−prime hyper ideal in a multiplicative hyperring r. a proper hyperideal p of r is an i−prime hyperideal if for a, b ∈ r with ab ⊆ p − ip implies a ∈ p or b ∈ p. we provide some characterizations of i−prime hyperideals. also we conceptualize and study the no tions 2−absorbing i−prime and n−absorbing i−prime hyperideals into multiplicative hyperrings as generalizations of prime ideals. a proper hyperideal p of a hyperring r is an n−absorbing i−prime hyperideal if for x1, · · · , xn+1 ∈ r such that x1 · · · xn+1 ⊆ p −ip, then x1 · · · xi−1xi+1 · · · xn+1 ⊆ p for some i ∈ {1, · · · , n + 1}. we study some properties of such generalizations. we prove that if p is an i−prime hyperideal of a hyperring r, then each of p/j , s^−1p, f(p), f^−1 (p), √ p and p[x] are i−prime hyperideals under suit able conditions and suitable hyperideal i, where j is a hyperideal contains in p. also, we characterize i−prime hyperideals in the decomposite hyperrings. moreover, we show that the hyperring with finite number of maximal hyperideals in which every proper hyperideal is n−absorbing i−prime is a finite product of fields.