三角代数上σ-三重可导映射的可加性

Additivity of σ-Triple Derivable Maps on Triangular Algebras

设U是一个三角代数,δ是U上的一个映射(无可加性假设),σ为U上的一个自同构.利用代数分解方法,证明了如果对任意的x,y,z∈U,有δ(xyz)=δ(x)yz+σ(x)δ(y)z+σ(x)σ(y)δ(z)成立,则δ是U上的一个可加的σ-三重导子.

Let U be a triangular algebra,δbe a mapping from U into itself(without the assumption of additivity),andσbe an automorphism of U.By using the method of algebraic decomposition,It is proved that ifδsatisfiedδ(xyz)=δ(x)yz+σ(x)δ(y)z+σ(x)σ(y)δ(z)for all x,y,z∈U,thenδis an additiveσ-triple derivation.