Commuting maps on rank-1 matrices over noncommutative division rings

Autor: Willian Franca, Nelson Louza
Rok vydání: 2017
Předmět:
Zdroj: Communications in Algebra. 45:4696-4706
ISSN: 1532-4125
0092-7872
DOI: 10.1080/00927872.2016.1278010
Popis: Let n≥3 be a natural number. Let Mn(𝔻) be the ring of all n×n matrices over a noncommutative division ring 𝔻. In the present paper, we will find the description of all additive mappings G:Mn(𝔻)→Mn(𝔻) such that [G(y),y] = G(y)y−yG(y) = 0 for all rank-1 matrix y. Precisely, we will prove that G(x) = λx+μ(x) for all x∈Mn(𝔻), where λ lies in the center of 𝔻 and μ is a central map.
Databáze: OpenAIRE