Maps preserving square-zero matrices on the algebra consisting of all upper triangular matrices |
| |
Authors: | Yanxia Zhao Xuansheng Wang |
| |
Institution: | Department of Mathematics , China University of Mining and Technology , Xuzhou, P.R. China |
| |
Abstract: | Let F be a field, T n (F) (respectively, N n (F)) the matrix algebra consisting of all n × n upper triangular matrices (respectively, strictly upper triangular matrices) over F. A ∈ T n (F) is said to be square zero if A 2 = 0. In this article, we firstly characterize non-singular linear maps on N n (F) preserving square-zero matrices in both directions, then by using it we determine non-singular linear maps on T n (F) preserving square-zero matrices in both directions. |
| |
Keywords: | square-zero matrices linear maps preserving square-zero matrices F-algebra |
|
|