A NOTE ON GENERALIZED DERIVATIONS AS A JORDAN HOMOMORPHISMS

Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x1, ..., xn) be a non central multilinear polynomial over C. If F(f(r1, ....

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Published in:Taehan Suhakhoe hoebo 2020, Vol.57 (3), p.709-737
Main Authors: Chandrasekhar, Arusha, Tiwari, Shailesh Kumar
Format: Article
Language:Korean
Online Access:Get full text
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Summary:Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x1, ..., xn) be a non central multilinear polynomial over C. If F(f(r1, ..., rn))G(f(r1, ..., rn)) - f(r1, ..., rn)T(f(r1, ..., rn)) = H(f(r1, ..., rn)2) for all r1, ..., rn ∈ R, then we describe all possible forms of F, G, H and T.
ISSN:1015-8634