Volume No. : 9
Issue No. : 4
Year : 2017
ISSN Print : 09754393
ISSN Online : 23492988
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Dr. C. Jaya Subba Reddy, G. Venkata Bhaskara Rao
Department of Mathematics, Sri Venkateswara University, Tirupati517502, Andhra Pradesh, India.
*Corresponding Author


DOI No: 10.5958/23492988.2017.00102.4
ABSTRACT:
Let R be a non commutative 2, 3torsion free prime ring and I be a non zero ideal of R. Let D(.,.):R×R?R be a symmetric left biderivation such that D(I,I)?I and d is a trace of D. If (i)[d(x),x]=0, for all x?I, (ii) [ d(x),x]?Z(R), for all x?I, then D=0. Suppose that there exists symmetric left biderivations D_1 (.,.):R×R?R and D_2 (.,.):R×R?R and B(.,.):R×R?R is a symmetric biadditive mapping, such that (i) D_1 (d_2 (x),x)=0, for all x?I, (ii) d_1 (d_2 (x) )=f(x), for all x?I, where d_1 and d_2 are the traces of D_1 and D_2 respectively and f is trace of B, then either D_1=0 or D_2=0. If D acts as a left (resp. right) Rhomomorphism on I, then D=0.

KEYWORDS:
Prime ring, Symmetric mapping, Trace, Biadditive mapping, Symmetric biadditive mapping, Symmetric biderivation, Symmetric left biderivation.

Cite:
C. Jaya Subba Reddy, G. Venkata Bhaskara Rao. Ideals and Symmetrc Left BiDerivations on Prime Rings. Research J. Science and Tech. 2017; 9(4): 601604.

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