(–1, 1) Rings without Nilpotent Elements - Hari babu, K.; Jayalakshmi, K. (International Journal of Engineering and Technology, 2018)
A ring of type 12(خ³,خ´)"> , was introduced by Albert and Kokoris [1,3] where in they have shown that a simple ring of 12(خ³,خ´)"> type is either associative or contains no idempotent other than 1. In this paper we obtain further results on the residual cases, to prove that a nonassociative (-1,1) rings satisfying (x, x, y)2 = 0, for all elements of the rings imply (x, x, y) = 0. But then indeed (-1,1) rings which have no nilpotent elements are associative and there by all such rings are division rings.