ИСТИНА

A key problem is that any Euler -- Lagrange operator satisfies Noether identities, which therefore must be separated into the trivial and non-trivial ones. These Noether identities can obey first-stage Noether identities, which in turn are subject to the second-stage ones, and so on. Thus, there is a hierarchy of Noether identities and higher-stage Noether identities which also must be separated into the trivial and non-trivial ones. This hierarchy of Noether and higher-stage Noether identities is described in the framework of a Grassmann-graded homology complex. Therefore Lagrangian theory of Grassmann-graded even and odd variables should be considered from the beginning.