Revista de la
Unión Matemática Argentina
Linear maps preserving Drazin inverses of matrices over local rings
Tugce Pekacar Calci, Huanyin Chen, Sait Halicioglu, and Guo Shile
Volume 62, no. 2 (2021), pp. 415–422

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Let $R$ be a local ring and suppose that there exists $a\in F^*$ such that $a^6\neq 1$; also let $T: M_n(R) \to M_m(R)$ 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 $M_n(R)$ to $M_m(R)$ preserving Drazin inverses of matrices.