Characterizations of regular and intra-regular ordered $\Gamma$-semihypergroups in terms of bi-$\Gamma$-hyperideals

Abstract

The concept of $\Gamma$-semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of $\Gamma$-semigroups. In this paper, we study the notion of bi-$\Gamma$-hyperideals in ordered $\Gamma$-semihypergroups and investigate some properties of these bi-$\Gamma$-hyperideals. Also, we define and use the notion of regular ordered $\Gamma$-semihypergroups to examine some classical results and properties in ordered $\Gamma$-semihypergroups.