Additive Maps on Matrix Algebras Preserving Invertibility or Singularity

We characterize the additive singularity preserving almost surjective maps on M n (F), the algebra of all n 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.