Additive maps on matrix algebras preserving invertibility or singularity

摘要

We characterize the additive singularity preserving almost surjective maps on M-n(F), the algebra of all n x n matrices over a field F with char F = 0. We also describe additive invertibility preserving surjective maps on M-n(F) and give examples showing that all the assumptions in these two theorems are indispensable.