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Additive n-commuting maps on semiprime rings
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2019-11-11 , DOI: 10.1017/s001309151900018x Cheng-Kai Liu
Proceedings of the Edinburgh Mathematical Society ( IF 0.7 ) Pub Date : 2019-11-11 , DOI: 10.1017/s001309151900018x Cheng-Kai Liu
Let R be a semiprime ring with the extended centroid C and Q the maximal right ring of quotients of R . Set [y , x ]1 = [y , x ] = yx − xy for x , y ∈ Q and inductively [y , x ]k = [[y , x ]k −1 , x ] for k > 1. Suppose that f : R → Q is an additive map satisfying [f (x ), x ]n = 0 for all x ∈ R , where n is a fixed positive integer. Then it can be shown that there exist λ ∈ C and an additive map μ : R → C such that f (x ) = λx + μ (x ) for all x ∈ R . This gives the affirmative answer to the unsolved problem of such functional identities initiated by Brešar in 1996.
中文翻译:
半素环上的加性 n 对易映射
让R 是一个质心延长的半素环C 和问 的商的最大右环R . 放 [是的 ,X ]1 = [是的 ,X ] =yx -xy 为了X ,是的 ∈问 和归纳[是的 ,X ]ķ = [[是的 ,X ]ķ -1 ,X ] 为了ķ > 1. 假设F :R →问 是一个满足 [F (X ),X ]n = 0 全部X ∈R , 在哪里n 是一个固定的正整数。则可以证明存在 λ ∈C 和一个加法图μ :R →C 这样F (X ) = λX +μ (X ) 对所有人X ∈R . 这对 Brešar 在 1996 年提出的此类功能性身份的未解决问题给出了肯定的答案。
更新日期:2019-11-11
中文翻译:
半素环上的加性 n 对易映射
让