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Research Journal of Science and Technology
Year : 2017, Volume : 9, Issue : 4
First page : ( 601) Last page : ( 604)
Print ISSN : 0975-4393. Online ISSN : 2349-2988.
Article DOI : 10.5958/2349-2988.2017.00102.4

Ideals and Symmetrc Left Bi-Derivations on Prime Rings

Dr. Reddy C. Jaya Subba*, Rao G. Venkata Bhaskara

Department of Mathematics, Sri Venkateswara University, Tirupati-517502, Andhra Pradesh, India

*Corresponding Author E-mail: cjsreddysvu@gmail.com

Online published on 12 June, 2018.

Abstract

Let R be a non commutative 2, 3-torsion free prime ring and I be a non zero ideal of R. Let Dd(.,.):R×RR be a symmetric left bi-derivation such that D(I,I)I and d is a trace of D. If (i)[d(x),x]= 0, for all x,ε I (ii) [d(x),x] ε Z(Rx), for all xε I then D =0. Suppose that there exists symmetric left bi-derivations D1d(.,.)R×RR and D2d(.,.)R×RR and Bd(.,.)R×RR is a symmetric bi-additive mapping, such that (i) D1 (d2;d(x),x) =0, for all x ε I (ii) d1 (d2;d(x),) = f(x), for all x ε I, where d1 and d2 are the traces of D1 and D2 respectively and f is trace of B, then either D1=0 or D2=0. If D acts as a left (resp. right) R -homomorphism on I, then D =0.

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Keywords

Prime ring, Symmetric mapping, Trace, Bi-additive mapping, Symmetric bi-additive mapping, Symmetric biderivation, Symmetric left bi-derivation.

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