Symmetric Reverse Bi-Derivations on Prime Rings Dr. Reddy C. Jaya Subba, M. Naik Ramakrishna* Department of Mathematics, S.V. University, Tirupati-517502, Andhra Pradesh, India *Corresponding Author E-mail: ramsanthu950@gmail.com
Online published on 12 January, 2017. Abstract Let R be a 2, 3-torsion free prime ring. Let D: (.,.): R X R → R and dbe a symmetric reverse bi-derivation and the trace of D respectively. If d is commuting orcentralizing on Rx. Then D= 0. Let D1: (.,.): R × R → R, b2: (.,.): R × R → R aresymmetric reverse bi-derivations and B(.,.): R × R → R be a symmetric bi-additive mapping. If D1(d2(x)x)=0 and d1(d2(x))=f(x), for all xɛR, where d1, d2 and f are the traces of D1, D2 and B. In this case either D1= 0 or D2= 0. Top Keywords Prime ring, Symmetric mapping, Trace, Symmetric bi-additive mapping, Symmetric biderivation, Symmetric reverse bi-derivation. Top |