 A graded commutative formula_16-algebra is isomorphic to the structure ring of a graded manifold with a body formula_3 if and only if it is the exterior algebra of some projective formula_16-module of finite rank.Note that above mentioned Batchelor's isomorphism fails to be canonical, but it often is fixed from the beginning.In this case, every trivialization chart formula_32 of the vector bundle formula_20 yields a splitting domain formula_34 of a graded manifold formula_2, where formula_36 is the fiber basis for formula_26.