Assosymmetric Rings with Weak Novikov Identity

Abstract

In this paper we show that in a non-associative 2-and 3-divisible prime assosymmetric ring R satisfying the weak Novikov identity (w,x,yz) = y (w,x,z), the square of every element of R is in the nucleus and then the non-zero idempotent e in R is the identity element of R.