On Pure Hyperideals In Ternary Semihypergroups

Abstract

This paper deals with a class of algebraic hyperstructures called ternarysemihypergroups, which are a generalization of ternary semigroups. In this paper weintroduce some special classes of hyperideals in ternary semihypergroups. Weintroduce the notions of pure hyperideals, weakly pure hyperideals, purely andpurely prime hyperideals and study some properties of them in ternarysemihypergroups and weakly regular ternary semihypergroups. The collection of allproper purely prime hyperideals of a ternary semihypergroup with zero istopologized.