2‐Prime Hyperideals of Multiplicative Hyperrings

Abstract

Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. A proper hyperideal I of R is called 2-prime if x ∘ y ⊆ I for some x , y ∈ R , then, x 2 ⊆ I or y 2 ⊆ I . The 2-prime hyperideals are a generalization of prime hyperideals. In this paper, we aim to study 2-prime hyperideals and give some results. Moreover, we investigate δ -2-primary hyperideals which are an expansion of 2-prime hyperideals.