Linear maps preserving r-potents of tensor products of matrices

Let Mn be the algebra of all n×n complex matrices and r≥2 a fixed integer. The aim of this paper is to characterize linear maps ϕ:Mm1⋯ml→Mm1⋯ml such that ϕ(A1⊗⋯⊗Al) is r-potent whenever A1⊗⋯⊗Al is r-potent.