Skew Derivations With Power Central-Values On Commutators

Skew Derivations With Power Central-Values On Commutators

陳弘遠(Hung-Yung Chen)

指導教授 ： 李秋坤

國立臺灣大學/理學院/數學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.01428

摘要

無資料

關鍵字

同構 ； 質環 ； 馬汀達爾除環 ； 斜導算 ； M-內部型

並列摘要

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.

並列關鍵字

Automorphism ； prime ring ； Martindale quotient ring ； skew derivation ； M-inner

參考文獻

[1] K.I. Beidar and M. Bresar, Extended Jacobson Density Theorem for Rings with

Derivations and Automorphisms, Israel J. Math., 122 (2001), 317-346.

Identities", Monographs and Textbooks in Pure and Applied Mathematics, 196.

[3] L. Carini and V.De Filippis, Commutators with power central values on a Lie

ideal, Paci c J. Math., 193(2) (2000), 269-278.