Commuting maps on rank-1 matrices over noncommutative division rings
Autor: | Willian Franca, Nelson Louza |
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Rok vydání: | 2017 |
Předmět: |
Ring (mathematics)
Algebra and Number Theory 010102 general mathematics Center (category theory) Natural number 010103 numerical & computational mathematics Division (mathematics) Rank (differential topology) 01 natural sciences Noncommutative geometry Combinatorics Matrix (mathematics) Division ring 0101 mathematics Mathematics |
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 |
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