Centralizing maps on invertible or singular matrices over division rings

被引：27
|
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 / 440卷
关键词：
Centralizing maps; Functional identities; Invertible matrices; Singular matrices; COMMUTING MAPS; PRIME-RINGS; FUNCTIONAL IDENTITIES; TRIANGULAR ALGEBRAS; INVOLUTION; MAPPINGS;
D O I：
10.1016/j.laa.2013.10.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let D be a division ring and let M-n(D) be the ring of all n x n matrices over D with center Z, where n >= 2 is an integer. We describe the additive map f : M-n(D) -> M-n(D) such that f(x)x - xf(x) is an element of Z for all invertible (singular) x is an element of M-n(D). (C) 2013 Elsevier Inc. All rights reserved.
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页码：318 / 324
页数：7
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