Quadri et al proved that if R is an associative ring satisfying the identity(x y)2 = x2 y2 for all x, y in R, then R is commutative. Many results have been proved for associative rings. This paper contains generalization of some results on nonassociative rings with unity. Jordan product type identities were takenin the center of nonassociative rings. Here x y = xy + yx is the Jordan product. The following identities satisfies the commutativity of a nonassociative ring with unity in the center.(i) (x y) ?U,
(ii) (x y)2 – (x y) ?U,(iii) (x y2) – (x2 y) ?U,(iv) (x y)2 – (x2 y2) ?U,
(v) (x2 y2)z2 – (x y)z?U,(vi) (x y)2z2 – (x y)z?U,(vii) (x y2)z – (x y)z?Uand
(viii) (x2 y2)z2 – (x y)z?U for all x, y, z in R.
Cite this article:
K. Madhusudhan Reddy. Nonassociative rings with some Jordan product identities in the center. Research J. Pharm. and Tech. 2016; 9(12): 2319-2321. doi: 10.5958/0974-360X.2016.00465.0