Resumen de Linear maps preserving Drazin inverses of matrices over local rings

Tugce Pekacar Calci, H. Chen, S. Halicioglu, G. Shile

• 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.