Additive maps on rank-s matrices. Issue 4 (3rd April 2017) - Xu, Xiaowei; Liu, Hanchao
Abstract : Let be the ring of all matrices over a field with . In this paper, it is proved that a map is additive if and only if for all rank- s matrices, where s is a fixed positive integer such that, which has been verified to be true for the case in [Xu X, Pei Y, Yi X. Additive maps on invertible matrices. Linear Multilinear Algebra. 2016;64:1283–1294]. Also, an example is provided showing that the conclusion will be incorrect if .