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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-sub semigroup, ternary Γ-sub semigroup generated by a subset, cyclic ternary Γ-sub semigroup of a ternary Γ-semigroup and cyclic ternary Γ-semigroup are introduced and characterized them
In section 3, we discussed some special elements of aternary Γ-semigroups and characterized them.