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Title: | Skew Derivations With Power Central-Values On Commutators |
Authors: | Hung-Yung Chen 陳弘遠 |
Advisor: | 李秋坤(Tsiu-Kwen Lee) |
Keyword: | 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, |
Publication Year : | 2005 |
Degree: | 碩士 |
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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38894 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 數學系 |
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