Some Properties of Weak$\mathrm{\Gamma }$-Hyperfilters in Ordered$\mathrm{\Gamma }$-Semihypergroups

Abstract

The main purpose of this paper is to study fundamental properties of weak Γ -hyperfilters on ordered Γ -semihypergroups that is a generalization of Γ -hyperfilters. Also, we investigate the relationship between weak Γ -hyperfilters and prime Γ -hyperideals in ordered Γ -semihypergroups. Finally, we introduce weak m , n - Γ -hyperfilters of ordered Γ -semihypergroups and conclude in paper with arising explicit theorems.