Abstract

Let R be a noncommutative prime ring equipped with an antiautomorphism f such that (i) [f(x^k), x^m] = 0, all x $\in$ R, where k, m are fixed positive integers. In this article, we establish that from (i) follows (ii) [f(x), x = 0, all x $\in$ R. More is to be said about the type of f and the structure of R.

中文翻译：

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广义功率交换反自同构

摘要

设R是一个非交换素环，它配备了一个反自同构 f 使得 (i) [ f ( x ^k ), x ^m ] = 0，所有x $\in$ R，其中k，m是固定的正整数。在本文中，我们确定从 (i) 遵循 (ii) [ f ( x ), x  = 0, all x $\in$ [R 。关于f的类型和R的结构还有更多要说的。