  Permutation modules are fundamental in the representation theory of symmetric
groups $\Sym_n$ and their corresponding Iwahori--Hecke algebras $\He =
\He(\Sym_n)$. We find an explicit combinatorial basis for the annihilator of a
permutation module in the "integral" case -- showing that it is a cell ideal in
G.E. Murphy's cell structure of $\He$. The same result holds whenever $\He$ is
semisimple, but may fail in the non-semisimple case.
