質環上的喬登τ-導算

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.