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Research Journal of Pharmacy and Technology
Year : 2016, Volume : 9, Issue : 12
First page : ( 2319) Last page : ( 2321)
Print ISSN : 0974-3618. Online ISSN : 0974-360X.
Article DOI : 10.5958/0974-360X.2016.00465.0

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(xy)2 = x2y2 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 xy = xy + yx is the Jordan product. The following identities satisfies the commutativity of a nonassociative ring with unity in the center.(i) (xy) ɛU, (ii) (xy)2-(xy) ɛU, (iii) (xy2)-(x2 ○ y) ɛU, (iv) (xy)2-(x2y2) ɛU, (v) (x2y2)z2-(xy)zɛU, (vi) (xy)2z2-(x ○ y)zɛU, (vii) (xy2)z-(x ○ y)zɛUand (viii) (x2y2)z2-(x ○ y)zɛU for all x, y, z in R.

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Keywords

Nonassociative ring, center, Char. ≠ n.

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