Linear maps preserving idempotents of tensor products of matrices

Let FF be a field of characteristic not 2 and MnMn the algebra of all n×nn×n matrices over FF. The aim of this paper is to characterize linear maps ϕ:Mm1⋯ml→Mm1⋯mlϕ:Mm1⋯ml→Mm1⋯ml such that ϕ(A1⊗⋯⊗Al)ϕ(A1⊗⋯⊗Al) is an idempotent whenever A1⊗⋯⊗AlA1⊗⋯⊗Al is an idempotent.