Associators in the Nucleus of Antiflexible Rings

In this paper, first we prove that if R is a semi prime third power associative ring of char ≠ 2 then either N = C or R is associative. Using this result we prove that if R is a simple third power associative antiflexible ring of char ≠ 2,3 satisfying (x, x, y) = k (y, x, x) for all x,y ? R, k ≠ 0 and 3
+ 2k + 1 ≠ 0 then either R is associative or nucleus equals center.