On some power joined T-semigroups

In this paper, we introduce commutative, archimedean, nonpotent Γ-semigroup, Putcha γ-semigroup and E-m Γ-semigroup. We prove that a finitely generated, commutative, nonpotent, archimedian Γ-semigroup is power joined. We also prove that if S is a commutative, nonpotent, archimedian Γ-semigroup, then, S is power joined if and only if every finitely generalized sub-Γ-semigroup H of S is archimedian. Thereafer, we obtain some equivalent conditions. Then, we prove that an archimedian nonpotent Γ-semigroup is power joined if and only if the structure Γ-group G_s=S/φ of S is periodic for some sεS; equivalently, it is true for all sεS. We also show that every medial Γ-semigroup S is a left and right Putcha Γ-semigroup and that every E-m Γ-semigroup is a right and left Putcha Γ-semigroup.