Nonlinear Jordan centralizer of strictly upper triangular matrices
Let ℱ be a field of zero characteristic, let Nn(ℱ) denote the algebra of n×n strictly upper triangular matrices with entries in ℱ, and let f:Nn(ℱ)→Nn(ℱ) be a nonlinear Jordan centralizer of Nn(ℱ),that is, a map satisfying that f(XY+YX)=Xf(Y)+f(Y)X, for all X, Y∈Nn(ℱ). We prove that f(X)=λX+η(X) wher...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2020-08-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.08.002/full/pdf |
| _version_ | 1797791631444803584 |
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| author | Driss Aiat Hadj Ahmed |
| author_facet | Driss Aiat Hadj Ahmed |
| author_sort | Driss Aiat Hadj Ahmed |
| collection | DOAJ |
| description | Let ℱ be a field of zero characteristic, let Nn(ℱ) denote the algebra of n×n strictly upper triangular matrices with entries in ℱ, and let f:Nn(ℱ)→Nn(ℱ) be a nonlinear Jordan centralizer of Nn(ℱ),that is, a map satisfying that f(XY+YX)=Xf(Y)+f(Y)X, for all X, Y∈Nn(ℱ). We prove that f(X)=λX+η(X) where λ∈ℱ and η is a map from Nn(ℱ) into its center 𝒵(Nn(ℱ)) satisfying that η(XY+YX)=0 for every X,Yin Nn(F). |
| first_indexed | 2024-03-13T02:21:33Z |
| format | Article |
| id | doaj.art-f180db12c6aa4473b7604eea9b7d199f |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:21:33Z |
| publishDate | 2020-08-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-f180db12c6aa4473b7604eea9b7d199f2023-06-30T09:27:54ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142020-08-01261/219720110.1016/j.ajmsc.2019.08.002Nonlinear Jordan centralizer of strictly upper triangular matricesDriss Aiat Hadj Ahmed0Centre Régional des Metiers d’Education et de Formation (CRMEF), Tangier, MoroccoLet ℱ be a field of zero characteristic, let Nn(ℱ) denote the algebra of n×n strictly upper triangular matrices with entries in ℱ, and let f:Nn(ℱ)→Nn(ℱ) be a nonlinear Jordan centralizer of Nn(ℱ),that is, a map satisfying that f(XY+YX)=Xf(Y)+f(Y)X, for all X, Y∈Nn(ℱ). We prove that f(X)=λX+η(X) where λ∈ℱ and η is a map from Nn(ℱ) into its center 𝒵(Nn(ℱ)) satisfying that η(XY+YX)=0 for every X,Yin Nn(F).https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.08.002/full/pdfJordan centralizerStrictly upper triangular matricesCommuting map |
| spellingShingle | Driss Aiat Hadj Ahmed Nonlinear Jordan centralizer of strictly upper triangular matrices Arab Journal of Mathematical Sciences Jordan centralizer Strictly upper triangular matrices Commuting map |
| title | Nonlinear Jordan centralizer of strictly upper triangular matrices |
| title_full | Nonlinear Jordan centralizer of strictly upper triangular matrices |
| title_fullStr | Nonlinear Jordan centralizer of strictly upper triangular matrices |
| title_full_unstemmed | Nonlinear Jordan centralizer of strictly upper triangular matrices |
| title_short | Nonlinear Jordan centralizer of strictly upper triangular matrices |
| title_sort | nonlinear jordan centralizer of strictly upper triangular matrices |
| topic | Jordan centralizer Strictly upper triangular matrices Commuting map |
| url | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.08.002/full/pdf |
| work_keys_str_mv | AT drissaiathadjahmed nonlinearjordancentralizerofstrictlyuppertriangularmatrices |