質環上的李導算

Abstract

令 R 是一個質環，Q_ml (R) 為其左極大商環，滿足 char R = 2 與 dim_C RC=4。令 δ∶ R→ Q_ml (R) 是一個李導算。則我們證明對每個 x∈R，δ(x)=d(x)+ϕ(x)+W(x)+ν(x) 其中 d∶ R→Q_ml (R) 是一個導算，ϕ∶ R→Q_ml (R) 是一個特殊形式的李導算，W∶ R→Q_ml (R) 是一個特殊形式的弱李導算，ν∶ R→C 是一個加性函數並滿足一個特別的關係式。

Let R be a prime ring with extended centroid C and maximal left ring of quotients Q_ml (R). Let δ∶ R→ Q_ml (R) be a Lie derivation. Suppose that charR=2 and dim_C RC=4. It is proved that δ(x)=d(x)+ϕ(x)+W(x)+ν(x) for all x∈R, where d∶ R→Q_ml (R) is a derivation, ϕ∶ R→Q_ml (R) is a Lie derivation of a special form, W∶ R→Q_ml (R) is a weak Lie derivation of a special form, and ν∶ R→C is an additive map satisfying a specific relation.