  Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether
identities which need not be independent, but satisfy first-stage Noether
identities, and so on. This construction is generalized to arbitrary
differential operators on a smooth fiber bundle. Namely, if a certain necessary
and sufficient condition holds, one can associate to a differential operator
the exact chain complex with the boundary operator whose nilpotency condition
restarts all the Noether identities characterizing the degeneracy of an
original differential operator.
