Nonlinear strong commutativity preserving maps on skew elements of prime rings with involution

被引：8

作者：

Liau, Pao-Kuei ^{[1
]}

Huang, Wei-Lu ^{[1
]}

Liu, Cheng-Kai ^{[1
]}

机构：

[1] Natl Changhua Univ Educ, Dept Math, Changhua 500, Taiwan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 09期

关键词：

Prime ring; Involution; Strong commutativity preserving; Functional identity (FI); LINEAR-MAPS; MATRIX ALGEBRAS; GENERALIZED DERIVATIONS; SEMIPRIME RINGS; LIE IDEALS; OPERATORS; MAPPINGS; PRODUCT; PAIRS;

D O I：

10.1016/j.laa.2011.10.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be a prime ring of characteristic not 2, with involution, with center Z(A) and with skew elements kappa. Suppose that f : kappa -> A is a map satisfying [f (x), f (y)] = [x, y] for all x, y is an element of kappa. Then there exists a map mu : kappa -> Z(A) such that f (x) = x + mu(x) for all x is an element of kappa or f (x) = -x + mu(x) for all x is an element of kappa except when A is an order in a 4, 9 or 16-dimensional central simple algebra. (C) 2011 Published by Elsevier Inc.

引用

页码：3099 / 3108

页数：10

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