Abstract
Let R be a nonassociative ring with center U. In this paper, it is shown that nonassociative ring R of char. ≠ 2 with unity is commutative if it satisfies any one of the following identities:
(i) (xy)x + x(xy) + y∈ U, (ii) (xy)2 - x2 y – xy2 - xy∈ U, (iii) (xy)2 - x2 y – xy2 - yx∈ U
(iv) (xy)2– xy2∈ U, (v) (xy)2– y2 x ∈ U, (vi) (x2y2)z2 – (xy)z ∈ U,
(vii) (x2y2)z2–(xy)z ∈ U for all x, y, and for fixed z in R.
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