• COMMUTATIVITY OF ASSOCIATIVE RINGS WITH (X, Y2) - (Y2, X), YX2Y=XY2X

Abstract

In this paper we have mainly focused on some theorems related to commutativity of associative and non associative rings. We prove that if R is an associative ring with unity satisfying (x, y²) - (y², x). ∀ x, y ϵ R, n ≥2 and xy³=y²xy ∀ x, y ϵ R, n ≥2. Then R is commutative ring and also I have mainly obtained two principles for a non associative ring to be a commutative ring.