代数的特殊高阶导子群

HIGHER DERIVATION GROUPS OF ALGEBRAS

设Φ是一个域,本文证明了Φ一代数A的全体长度为k的高阶导子的集合HDerkΦ(A)关于高阶导子乘法构成一个群.进而给出了HDerkΦ(A)的特殊子群及其商群结构.

Let Φ be a field and A a Φ-algebra. The set of all higher derivations with length k of A is proved to be a group with respect to the usual multiplication. Furthermore, We investigate the special subgroup of HDerΦk(A) and its quotient group.