Nonsurjective zero product preservers between matrix spaces over an arbitrary field
Nonsurjective zero product preservers between matrix spaces over an arbitrary field
AbstractA map Φ between matrices is said to be zero product preserving if Φ(A)Φ(B)=0wheneverAB=0.In this paper, we give concrete descriptions of an additive/linear zero product preserver Φ:Mn(F)→Mr(F) between matrix algebras of different dimensions over an arbitrary field F, and n≥2. In particular, we show that if Φ is linear and …