Commuting Values of Generalized Derivations on Multilinear Polynomials |
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Authors: | Asma Ali Faiza Shujat |
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Institution: | Department of Mathematics , Aligarh Muslim University , Aligarh , India |
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Abstract: | Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, U the right Utumi quotient ring of R, f(x 1,…, x n ) a noncentral multilinear polynomial over K, and G a nonzero generalized derivation of R. Denote f(R) the set of all evaluations of the polynomial f(x 1,…, x n ) in R. If G(u)u, G(v)v] = 0, for any u, v ∈ f(R), we prove that there exists c ∈ U such that G(x) = cx, for all x ∈ R and one of the following holds: 1. f(x 1,…, x n )2 is central valued on R; 2. R satisfies s 4, the standard identity of degree 4. |
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Keywords: | Generalized derivation Prime ring |
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