On maps characterized by action on equal products
On maps characterized by action on equal products
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在以平等产品行动为特征的地图上
DOI：
10.1016/j.jalgebra.2018.06.022
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发表时间：
2018
影响因子：
0.9
通讯作者：
Louisa Catalano
中科院分区：
文献类型：
--
作者：
Louisa Catalano
设D是特征不同于2的除环.本文描述了一个可加映射f，它满足恒等式f（x）y+ xf（y）= l，对任意x，y∈ D，使得xy = a，其中l，a∈ D且a非零.此外，对于非零m，k∈ D，我们将描述满足恒等式f（x）f（y）= m的加法双射f，对于每个x，y∈ D使得xy = k;这个描述是Chebotar，Ke，Lee，and Shiao在2005年提出的一个问题的解决方案。
Let D be a division ring with characteristic different from 2. In this paper we will describe an additive map f satisfying the identity f (x) y+ x f (y)= l for every x, y∈ D such that x y= a, where l, a∈ D and a is nonzero. Additionally, for nonzero m, k∈ D, we will describe the additive bijection f satisfying the identity f (x) f (y)= m for every x, y∈ D such that x y= k; this description is the solution to a problem posed by Chebotar, Ke, Lee, and Shiao in 2005.