Generalized derivations with Engel condition on multilinear polynomials |
| |
Authors: | Vincenzo De Filippis |
| |
Institution: | (1) DI.S.I.A., Faculty of Engineering, University of Messina, Contrada Di Dio, 98166 Messina, Italy |
| |
Abstract: | Let R be a prime ring with extended centroid C, δ a nonzero generalized derivation of R, f(x
1, ..., x
n
) a nonzero multilinear polynomial over C, I a nonzero right ideal of R and k ≥ a fixed integer.
If δ(f(r
1, ..., r
n
)), f(r
1, ..., r
n
)]
k
= 0, for all r
1, ..., r
n
∈ I, then either δ(x) = ax, with (a-γ)I = 0 and a suitable γ ∈ C or there exists an idempotent element e ∈ soc(RC) such that IC = eRC and one of the following holds
(1) if char(R) = 0 then f(x
1, ..., x
n
) is central valued in eRCe
(2) if char(R) = p > 0 then is central valued in eRCe, for a suitable s ≥ 0, unless when char(R) = 2 and eRCe satisfies the standard identity s
4
(3) δ(x) = ax−xb, where (a+b+α)e = 0, for α ∈ C, and f(x
1, ..., x
n
)2 is central valued in eRCe. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|