Vanishing Derivations and Co-Centralizing Generalized Derivations on Multilinear Polynomials in Prime Rings
| Autor: | Emine Albaş, Basudeb Dhara, Nurcan Argaç |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 44:1905-1923 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2015.1027393 |
| Popis: | Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x1,…, xn) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) − f(r)G(f(r))) = 0 for all r = (r1,…, rn) ∈ Rn, then one of the following holds: There exist a, p, q, c ∈ U and λ ∈C such that F(x) = ax + xp + λx, G(x) = px + xq and d(x) = [c, x] for all x ∈ R, with [c, a − q] = 0 and f(x1,…, xn)2 is central valued on R;There exists a ∈ U such that F(x) = xa and G(x) = ax for all x ∈ R;There exist a, b, c ∈ U and λ ∈C such that F(x) = λx + xa − bx, G(x) = ax + xb and d(x) = [c, x] for all x ∈ R, with b + αc ∈ C for some α ∈C;R satisfies s4 and there exist a, b ∈ U and λ ∈C such that F(x) = λx + xa − bx and G(x) = ax + xb for all x ∈ R;There exist a′, b, c ∈ U and δ a derivation of R such that F(x) = a′x + xb − δ(x), G(x) = bx + δ(x) and d(x) = [c, x... |
| Databáze: | OpenAIRE |
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