Strong commutativity preserving maps on subsets of matrices that are not closed under addition

被引：21
|
作者：
Liu, Cheng-Kai [1 ]
机构：
[1] Natl Changhua Univ Educ, Dept Math, Changhua 500, Taiwan
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 458卷
关键词：
Strong commutativity preserving maps; Invertible matrices; Singular matrices; GENERALIZED DERIVATIONS; SEMIPRIME RINGS; PRIME-RINGS; LIE IDEALS;
D O I：
10.1016/j.laa.2014.06.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let M-n(D) be the ring of all n x n matrices over a division ring D, where n >= 2 is an integer and let GL(n)(D) be the set of all invertible matrices in WILD). We describe maps f : GL(n)(D) -> M-n(D) such that [f (x), f (y)] = [x, y] for all x, y is an element of GL(n)(D). The analogous result for singular matrices is also obtained. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：280 / 290
页数：11
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