三角代数上的一类非全局三重可导映射
A Class of Non-global Triple Derivable Maps on Triangular Algebras
设T=Tri (A,M,B)为三角代数,Q={T∈T:T2=0}且δ:T→T是一个映射(没有可加或线性假设).证明了:如果对任意A,B,C ∈T且ABC ∈Q,有δ(ABC)=δ(A)BC+Aδ(B)C+ABδ(C),则δ是一个可加导子.作为应用,得到了上三角矩阵代数和套代数上此类非全局三重可导映射的具体形式.
Let T=Tri(A, M, B) be a triangular algebra, and Q={T∈T:T2=0}. We prove that if a map δ:T→T satisfies δ(ABC)=δ(A)BC+Aδ(B)C+ABδ(C) for any A, B, C ∈ T with ABC ∈ Q, then δ is an additive derivation.
三角代数 / 三重可导映射 / 平方零元 {{custom_keyword}} /
triangular algebra / triple derivable map / square zero element {{custom_keyword}} /
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国家自然科学基金资助项目(11471199)
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