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Additive maps on matrix algebras preserving invertibility or singularity
Fošner, Ajda ; Šemrl, Peter
We characterize the additive singularity preserving almost surjective maps on ▫$M_n(F)$▫, the algebra of all ▫n\times 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.
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