导子的局部特征

A Full-derivable Point on Triangular Algebras

设T为三角代数,如果对每一个从T到它自身的可加映射δ在Z点处可导,得出δ为导子,则称元素Z∈T是T的全可导点。该文主要用纯代数理论证明了P=(Ι1 Χ0 0 0)是一个全可导点。

Let T be a triangular algebra.We say that an element Z∈T is a full-derivable point of T if every additive map δ from T into itself derivable at Z is a derivation.In this paper,we will use a pure algebraic approach to prove that P=[Ι1 Χ0 0 0]is a full-derivable point.