指導教授：李秋坤臺灣大學：數學研究所林政輝Lin, Jheng-HueiJheng-HueiLin2014-11-302018-06-282014-11-302018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/264004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.口試委員會審定書 ....................i 誌謝 ....................ii 中文摘要 ....................iii 英文摘要 ....................iv 目錄 ....................v §0. Introduction ....................1 §1. Preliminaries ....................2 §2. Main Theorems ....................5 References ....................14873894 bytesapplication/pdf論文公開時間：2014/07/22論文使用權限：同意有償授權(權利金給回饋學校)質環喬登τ-導算反自同構泛函恆等式GPIPI雙邊極大商環thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264004/1/ntu-103-R01221012-1.pdf