  We consider various definitions of non-lc ideal sheaves -- generalizations of
the multiplier ideal sheaf which define the non-lc (non-log canonical) locus.
We introduce the maximal non-lc ideal sheaf and intermediate non-lc ideal
sheaves and consider the restriction theorem for these ideal sheaves. We also
begin the development of the theory of a characteristic p>0 analog of maximal
non-lc ideals, utilizing some recent work of Blickle.
