Linear maps preserving Drazin inverses of matrices over local rings

Authors

  • Tuğçe Pekacar Çalcı Department of Mathematics, Ankara University, Ankara, Turkey
  • Huanyin Chen Department of Mathematics, Hangzhou Normal University, Hangzhou, China
  • Sait Halicioglu Department of Mathematics, Ankara University, Ankara, Turkey
  • Guo Shile Fuqing Branch of Fujian Normal University, Fuqing, China

DOI:

https://doi.org/10.33044/revuma.1858

Abstract

 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.

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Published

2021-11-23

Issue

Vol. 62 No. 2 (2021)

Section

Article

License

Copyright (c) 2022 Tuğçe Pekacar Çalcı, huanyin chen, sait halicioglu, guo shile

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