Square-free decomposition in fields of positive characteristic

[todoseaportuprima]

Hi everyone,

I have the following doubt. Suppose K is a field of characteristic p>0 and f(X_1,...,X_n) a multivariate polynomial with coefficients in K such that deg(f) < p.

Is it true that f admits a square-free descomposition? I mean, with such hypothesis: can the usual algorithm for characteristic 0 be adapted to prove this without asking for the field K to be perfect?

Thanks a lot,
Peter