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Title: | 質環上的喬登τ-導算 Jordan τ-derivations of Prime rings |
Authors: | Jheng-Huei Lin 林政輝 |
Advisor: | 李秋坤(Tsiu-Kwen Lee) |
Keyword: | 質環,喬登τ-導算,反自同構,泛函恆等式,GPI,PI,雙邊極大商環, Prime ring,Jordan  τ-derivation,Anti-automorphism,Functional identity,GPI,PI,Maximal symmetric ring of quotients, |
Publication Year : | 2014 |
Degree: | 碩士 |
Abstract: | 我們將研究質環上喬登τ-導算的結構。明確地說,令R是一個非交換的質環,Qms(R)是其雙邊極大商環,且τ為R上頭的一個反自同構。令δ:R→Qms(R) 為一個喬登τ-導算。我們證明存在一個a ∈ Qms(R) 使得對於所有 x ∈ R 都有δ(x)=ax^τ-xa 如果以下任一條件成立:
(一) R不是GPI環; (二) R是一個可除環除了char R ≠=2 且 dim_{C} R=4; (三) R是中心封閉的GPI環且特徵不為二; (四) R是PI環且特徵不等於二。 In the thesis we study the structure of Jordan τ-derivations of prime rings. Precisely, let R be a noncommutative prime ring with Qms(R) the maximal symmetric ring of quotients of R and let τ be an anti-automorphism of R. Let δ:R→Qms(R) be a Jordan τ-derivation. We show that there exists a ∈ Qms(R) such that δ(x) = ax^τ-xa for all x ∈ R if one of the following conditions holds: (1) R is not a GPI-ring. (2) R is a division ring except when charR =/= 2 and dim_{C} R = 4. (3) R is a centrally closed GPI-ring with charR =/= 2. (4) R is a PI-ring with charR =/= 2. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58185 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 數學系 |
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ntu-103-1.pdf Restricted Access | 853.41 kB | Adobe PDF |
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