Some Properties of WeakΓ-Hyperfilters in OrderedΓ-Semihypergroups

Abstract

The main purpose of this paper is to study fundamental properties of weak$\mathrm{\Gamma }$-hyperfilters on ordered$\mathrm{\Gamma }$-semihypergroups that is a generalization of$\mathrm{\Gamma }$-hyperfilters. Also, we investigate the relationship between weak$\mathrm{\Gamma }$-hyperfilters and prime$\mathrm{\Gamma }$-hyperideals in ordered$\mathrm{\Gamma }$-semihypergroups. Finally, we introduce weak$\left(m,n\right)$-$\mathrm{\Gamma }$-hyperfilters of ordered$\mathrm{\Gamma }$-semihypergroups and conclude in paper with arising explicit theorems.