SOME RESULTS ON PRIME ASSOSYMMETRIC RINGS
With the help of this paper, we want to show that 2 – and 3 – divisible Assosymmetric ring R is sub direct sum of semi prime associative ring and semi prime commutative ring also if R is a 2 – and 3 – divisible prime assosymmetric ring then R must be either Associative or Commutative. 2 – and 3 – divisible prime assosymmetric ring R is power associative, that is, (x, x, x) = 0 And 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.
Assosymmetric ring, Prime ring, divisible ring, Weak Novikov identity , 2- and 3- divisible prime assosymmetric ring.