J-hyperideals and related generalizations ‎in ‎ ‎multiplicative ‎hyperrings

Abstract

‎In this paper‎, ‎we define the concept of $J$-hyperideals which is a generalization of $n$-hyperideals‎. ‎A proper hyperideal $I$ of a multiplicative hyperring $R$ is said to be a $J$-hyperideal if $x,y\in R$ such that $x \circ y \subseteq I$‎, ‎then either $x \in J(R)$ or $y \in I$‎. ‎We study and investigate the behavior of the $J$-hyperideals to introduce several results‎. ‎Moreover‎, ‎we extend the notion of $J$-hyperideals to quasi $J$-hyperideals and 2-absorbing $J$-hyperideals‎. ‎Various characterizations of them are provided‎.

Keywords

• $j$-hyperideal‎
• ‎quasi $j$-hyperideal‎
• ‎2-absorbing $j$-hyperideal