C-Γ-hyperideal Theory in Ordered Γ-semihypergroups

Abstract

Abstract. Our purpose in this article is to characterize the properties of C-Γ-hyperideals in ordered Γ-semihypergroups. As an application of the results of this paper, the corresponding results of ordered semihypergroups can also be obtained by moderate modification. Keywords: C--hyperideal;-hyperideal, ordered -semihypergroup; regular; semihypergroup; IntroductionThe formal study of semigroups began in the early 20th century. As a generalization of semigroups, the notion of a Γ-semigroup was first introduced by Sen Algebraic hyperstructures are a suitable generalization of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of hyperstructure was first introduced by Marty [15] at the eighth Congress of Scandinavian Mathematicians in 1934. Since then, several books have been published on this topic, for example see [16][17][18][19]. Ameri and Hoskova [20] studied the fuzzy continuous polygroup as a fuzzy