*-素环上的广义导子

R是2-扭自由*-素环,L是R上的平方封闭的非零*-Lie理想.f,g是R上的广义导子,d,h分别为f,g的非零伴随导子,有(i)f(u)v=ug(v),(ii)f(uv)-uv∈Z,(iii)f(u)f(v)-uv∈Z,u,v∈L,若d,h≠0,则UZ.

*-素环上(σ,τ)-导子的简单性质

R是2-扭自由*-素环,U是平方封闭的*-Lie理想.证明了一些关于*-素环的平方封闭的*-Lie理想上(σ,τ)-导子的简单性质.

Some Conditions of Central Lie Ideal

Let di（1≤ i≤n）, 51,52, 53 be nonzero derivations of a prime ring R with char R ≠ 2. Suppose that U is a Lie ideal such that u2 ∈ U for all u ∈ U. In this paper, we prove that U [U→] Z（R） when one of the following holds： （1） d1（x1）d2（x2）,… ,dn（xn）∈Z（R） （2） δ3（y）δ1（x） = δ2（x）δ3（y）. Further, if g is a Lie ideal and a subring then （3） δ1（x）δ2（y） ＋δ2（x）δ1（y） ∈ Z（R） for all xi,x,y ∈ U.

Lie Ideals in AF C~*-Algebras

We study Lie ideals in unital AF C^＊-algebras. It is shown that if a linear manifold L in an AF C^＊-algebra A is a closed Lie ideal in A, then there exists a closed associative ideal I and a closed subalgebra EI of the canonical masa D of A such that [A,I]^- belong to L belong to I ＋ EI, and that every closed subspace in this form is a closed Lie ideal in A.