Nonassociative rings with some jordan product identities in the center Reddy K. Madhusudhan* Department of Mathematics, School of Advanced Sciences, VIT University, Vellore-632 014, Tamil Nadu *Corresponding Author E-mail: drkmsreddy@yahoo.in
AMS Classifications: 17D05, 17D15 Online published on 2 March, 2017. Abstract 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) ɛU, (ii) (x ○ y)2-(x ○ y) ɛU, (iii) (x ○ y2)-(x2 ○ y) ɛU, (iv) (x ○ y)2-(x2 ○ y2) ɛU, (v) (x2 ○ y2)z2-(x ○ y)zɛU, (vi) (x ○ y)2z2-(x ○ y)zɛU, (vii) (x ○ y2)z-(x ○ y)zɛUand (viii) (x2 ○ y2)z2-(x ○ y)zɛU for all x, y, z in R. Top Keywords Nonassociative ring, center, Char. ≠ n. Top |