Published January 1, 2021
| Version v1
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LINEAR MAPS PRESERVING DRAZIN INVERSES OF MATRICES OVER LOCAL RINGS
- 1. Ankara Univ, Dept Math, Ankara, Turkey
- 2. Hangzhou Normal Univ, Dept Math, Hangzhou, Peoples R China
- 3. Fujian Normal Univ, Fuqing Branch, Fuqing, Peoples R China
Description
Let R be a local ring and suppose that there exists a is an element of F* such that a(6) not equal 1; also let T : M-n(R) -> 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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