  The well-known Mather-Yau theorem says that the isomorphism type of the local
ring of an isolated complex hypersurface singularity is determined by its
Tjurina algebra. It is also well known that this result is wrong as stated for
power series f in K[[x]] over fields K of positive characteristic. In this note
we show that, however, also in positive characteristic the isomorphism type of
an isolated hypersurface singularity f is determined by an Artinian algebra,
namely by a "higher Tjurina algebra" for sufficiently high index, for which we
give an effective bound. We prove also a similar version for the "higher Milnor
algebra" considered as K[[f]]-algebra.
