具泛導算之中心恆等式

Abstract

令R是一個質環且dimC RC > 4, 令D,G是R的泛導算, 令m, n是固定的正整數.然後D(xm)xn− xnG(xm) ∈C 若且爲若以下兩個條件成立:(1) 存在w 屬於Q, R的Martindale 對稱除環, 使得D(x) = xw且G(x) = wx 對於所有的x屬於R (2)w屬於C或者是xm和xn是C相依的對於所有的x屬於R. 我們也將討論非交換李理想的例.

Let R be a prime ring and dimC RC > 4, let D,G be two generalized derivations of R, and let m, n be two fixed positive integers. Then D(xm)xn−xnG(xm) ∈C for all x ∈R iff the following two conditions hold: (1) There exists w 2 Q, the symmetric Martindale quotient ring of R, such that D(x) = xw and G(x) = wx for all x ∈R; (2) either w ∈C, or xm and xn are C-dependent for all x ∈R. We also consider the situation of noncommutative Lie ideals.