Commuting maps on rank-1 matrices over noncommutative division rings

被引:12
|
作者
Franca, Willian [1 ]
Louza, Nelson [1 ]
机构
[1] Univ Fed Juiz de Fora, Dept Matemat, BR-36036900 Juiz De Fora, MG, Brazil
关键词
Commuting maps; division rings; functional identities; rank-1; matrices;
D O I
10.1080/00927872.2016.1278010
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let n >= 3 beanaturalnumber. Let M-n(D) be theringofall n x n matrices over a noncommutative division ring D. In the present paper, we will find the description of all additive mappings G : M-n(D) -> M-n(D) such that [G(y), y] = G(y)y - yG(y) = 0 for all rank-1 matrix y. Precisely, wewillprovethat G(x) = lambda x + mu(x) for all x epsilon M-n(D), where lambda lies inthecenterof D and mu is acentral map.
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页码:4696 / 4706
页数:11
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