IDEALS WITH SYMMETRIC REVERSE BI-DERIVATIONS ON PRIME AND SEMIPRIME RINGS
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Published:
Jul 30, 2017
Keywords:
Prime ring, Semiprime ring, Symmetric mapping, Bi-additive mapping, Symmetric bi-additive mapping, Trace, Symmetric bi- derivation, Symmetric reverse bi-derivation.
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Abstract
Let be a 2 and 3-torsion free non-commutative prime ring and be a nonzero ideal of . Suppose there exist a symmetric reverse bi-derivations and such that , for all , where and are the traces of and respectively. In this case either or and be a 2-torsion free semiprime ring and be a nonzero ideal of . Let be a symmetric reverse bi-derivation such that . If is a trace of such that , for all , then on .
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