  Combining the Batchelor theorem and the Serre-Swan theorem, we come to that,
given a smooth manifold $X$, a graded commutative $C^\infty(X)$-algebra $\cA$
is isomorphic to the structure ring of a graded manifold with a body $X$ iff it
is the exterior algebra of some projective $C^\infty(X)$-module of finite rank.
In particular, it follows that odd fields in field theory on a smooth manifold
$X$ can be represented by graded functions on some graded manifold with body
$X$.
