A Note on Two Classes of Hyperideals

Abstract

Let R be a commutative multiplicative hyperring with 1. In this paper, we define the concepts of r-hyperideal and n-hyperideal of the hyperring R which are two new classes of hyperideals. Several properties of them are provided. A hyperideal I of a multiplicative hyperring R is called an r-hyperideal of R, if for all x, y ∈ R, xoy ⊆ I and ann(x) = {0}, then y ∈ I. Also, a hyperideal I of a multiplicative hyperring R is called an n-hyperideal of R, if for all x, y ∈ R, xoy ⊆ I and x ∉ r(0), then y ∈ I.

Key words and phrases. Prime hyperideal, r-hyperideal, n-hyperideal, Hyperring.

2000 Mathematics Subject Classification. 20N20