Linear maps preserving Drazin inverses of matrices over local rings

T.P. Calci ^[1] ; H. Chen ^[2] ; S. Halicioglu ^[1] ; G. Shile ^[3]
1. [1] Ankara University
  
  Ankara University
  
  Turquía
2. [2] Hangzhou Normal University
  
  Hangzhou Normal University
  
  China
3. [3] Fujian Normal University
  
  Fujian Normal University
  
  China
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Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 2, 2021, págs. 415-422
Idioma: inglés
DOI: 10.33044/revuma.1858
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Resumen
- Let R be a local ring and suppose that there exists a ∈ F∗ such that a 6 6= 1; also let T : Mn(R) → Mm(R) be a linear map preserving Drazin inverses. Then we prove that T = 0 or n = m and T preserves idempotents. We thereby determine the form of linear maps from Mn(R) to Mm(R) preserving Drazin inverses of matrices.