Structure and Study of Elements in Ternary Γ-Semigroups

In this paper we introduce the notion of a ternary Γ- semigroup is introduced and some examples are given. Further the terms commutative ternary Γ-semigroup, quasi commutative ternary Γ-semigroup, normal ternary Γ- semigroup, left pseudo commutative ternary Γ-semigroup, right pseudo commutative ternary Γ-semigroup are introduced and characterized them. In section 2, the terms; ternary Γ-subsemigroup, ternary Γ-subsemigroup generated by a subset, cyclic ternary Γ-subsemigroup of a ternary Γ-semigroup and cyclic ternary Γ-semigroup are introduced and characterized them In section 3, we discussed some special elements of a ternary Γ-semigroups and characterized them