On 0-Minimal (0,2)-Bi-Hyperideal of Ordered Semihypergroups

Samkhan Hobanthad

Abstract

Focusing on the ordered semihypergroup, the goal is to find conditions of minimality of left (right) hyperideal, bi-hyperideal and $(0,2)$-hyperideal in ordered semihypergroups. The study begins by examining basic properties of $(0,2)$-hyperideal and bi-hyperideal. Using such knowledge demonstrates that if $ A $ is a $0$-minimal $(0,2)$-bi-hyperideal of an ordered semihypergroup $H$ with zero, then either $(A^{2}]=\left\lbrace 0\right\rbrace$ or $A$ is a left $0$-simple.