On the structure of quasi-hyperideals and bi-hyperideals in ternary semihypergroups

This paper deals with a class of algebraic hyperstructures called ternary semihypergroups, which are a generalization of ternary semigroups. Our main purpose of this paper is to introduce and study the notions of quasi-hyperideal and bi-hyperideal in ternary semihypergroups. The structure of ternary semihypergroups through the quasi- and bi-hyperideals is studied and some characterizations are given. Also, we introduce the notion of generalized bi-hyperideals. Several kinds of them are investigated.