N(A)-ternary semigroups

T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A    (2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4 are equivalent, where No(A) = The set of all A-potent elements in T, N1(A) = The largest ideal contained in No(A), N2(A) = The union of all A-potent ideals. If A is a semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A) = N1(A) = N2(A). It is also proved that if A is an ideal of a ternary semigroup such that N0(A) = A then A is a completely semiprime ideal. Further it is proved that if A is an ideal of ternary semigroup T then R(A), the divisor radical of A, is the union of all A-divisor ideals in T. In a N(A)ternary semigroup it is proved that R(A) = N1(A). If A is a semipseudo symmetric ideal of a ternary semigroup T then it is proved that S is an N(A)ternary semigroup iff R(A) = N0(A). It is also proved that if M is a maximal ideal of a ternary semigroup T containing a pseudo symmetric ideal A then M contains all A-potent elements in T or T\M is singleton which is A-potent.