关于三角代数上的广义Engel条件

Generalized Engel condition of triangular algebra

设R是有单位元的交换环,A,B是R上酉代数,M是非零(A,B)-酉双模。D是三角代数T上的导子。本文刻画了三角代数上满足广义Engel条件[[…[[D(Xm)Xn-XpG(Xq),Xn1],Xn2],…],Xnk]=0和[D(X),X]kX-X[G(X),X]k=0的导子的结构。

Let R be a commutative ring with identity element,A,B be unital algebras over R,M be a nonzero unital(A,B)-bimodule,and D be a derivation of triangular algebra T.In this paper,we investigate the structure of the derivation D of T,satisfying either of the generalized Engel condition…D X m,X n 1,X n 2,…,X n k=0 or[[…[[D(X m)X n-X p G(X q),X n 1],X n 2],…],X n k]=0,where m,n,p,q,n 1,n 2,…,n k are any positive integers.