(Weakly) $(\hat{I}\pm ,{\hat{I}}^2)$-prime hyperideals in commutative multiplicative hypeering

Abstract

Let $H$ be a commutative multiplicative hyperring and $\hat{I}\pm ,{\hat{I}}^2\in {\mathbb{Z}}^{+}$. A proper hyperideal $P$ of $H$ is called (weakly) $(\hat{I}\pm ,{\hat{I}}^2)$-prime if $x^{\hat{I}}\pm \circ y\subseteq P$ for $x,y\in H$ implies $x^2\subseteq P$ or $y\in P$. In this paper, we aim to investigate (weakly) $(\hat{I}\pm ,{\hat{I}}^2)$-prime hyperideals and then we present some properties of them.