  We study the annihilator of the cokernel of a map of free Z/2-graded modules
over a Z/2-graded skew-commutative algebra in characteristic 0 and define
analogues of its Fitting ideals. We show that in the ``generic'' case the
annihilator is given by a Fitting ideal, and explain relations between the
Fitting ideal and the annihilator that hold in general. Our results generalize
the classical Fitting Lemma, and extend the key result of Green [1999]. They
depend on the Berele-Regev theory of representations of general linear Lie
super-algebras.
