Skew Derivations With Power Central-Values On Commutators
Date Issued
2005
Date
2005
Author(s)
Chen, Hung-Yung
DOI
en-US
Abstract
In the thesis we study the problem concerning skew derivations with
power central-values on commutators in prime rings. Precisely, we
prove the following two main results.
Main Theorem 1. Let R be a prime ring with charR 6= 2, an
automorphism of R, and d a -derivation of R. If [d([x; y]); [x; y]]n = 0
for all x; y 2 R, then either d = 0 or R is a commutative ring.
Main Theorem 2. Let R be a prime ring, with an automorphism ,
and d a nonzero -derivation of R. Suppose that [d(x); x]n 2 Z(R) for
all x 2 R. If either charR = 0 or charR > n, then dimC RC 4.
As a corollary to Main Theorem 1, we have the following result.
Corollary. Let R be a prime ring with charR 6= 2, an automorphism
of R, L a noncentral Lie ideal of R, and d a -derivation of R. If
[d(x); x]n = 0 for all x 2 L, then either d = 0 or R is a commutative
ring.
2000 Mathematics Subject Classi cation. 16R53, 16R60, 16N60.
Key words and phrases. Automorphism, prime ring, Martindale quotient ring,
skew derivation, M-inner.
Subjects
同構
質環
馬汀達爾除環
斜導算
M-內部型
Automorphism
prime ring
Martindale quotient ring
skew derivation
M-inner
Type
thesis