半素环中的n-Centralizing映射

讨论半素环中n-centralizing映射是n-comm uting映射的一些条件. 利用平方封闭加法子群的线性化技巧证明了若对半素环R做适当的加法扭限制, 对R上的导子d, 若d_k在R的一个平方封闭的加法子群U上是n-centralizing的, 则它在U上也是n-commuting的.

n-Centralizing mappings in semiprime rings

We consider the conditions in case that a n-centralizing mapping in a simiprime ring is n-commuting. By using linearization in an additive subgroup of R whice is closed under squares, we conclude that with suitably-restricted additive torsion, for d a derivation in a semiprime ring R, if d_kis n-centralizing on U, an additive subgroup of R closed under squares, then it must be n-commuting on U.