Generalized Jordan n-derivations of unital algebras with idempotens
Generalized Jordan n-derivations of unital algebras with idempotens
复制标题
幂等单位代数的广义 Jordan n 导数
DOI：
10.1155/2021/9997646
复制
发表时间：
2021
影响因子：
1.4
通讯作者：
Xinfeng Liang
中科院分区：
文献类型：
--
作者：
Xinfeng Liang
设A是2-挠自由单位交换环R上的幂等元代数，S：A->；A是伴随着Jordan n-导子J的任意广义Jordan n-导子.我们证明了在较弱的条件下，每个广义Jordan n-导子S都是S(X)=\lambda x+J(X)的形式.作为应用，我们给出了具有幂等元的单位代数的经典例子：三角代数、矩阵代数、套代数和所有有界线性算子的代数在n=2条件下的广义Jordan导子的刻划，推广了一些已有的结果。
Let A be a unital algebra with idempotent e over a 2-torsionfree unital commutative ring R and S:A->A be an arbitrary generalized Jordan n-derivation associated with a Jordan n-derivation J. We show that, under mild conditions, every generalized Jordan n-derivation S is of the form S(x)=\lambda x+J(x) in the current work. As an application, we give a description of generalized Jordan derivations for the condition n=2 on classical examples of unital algebras with idempotents: triangular algebras, matrix algebras, nest algebras, and algebras of all bounded linear operators, which generalize some known results.