Invariant tensors and partial differential equations

We consider tensors with coefficients in a commutative differential algebra $A$. Using the Lie derivative, we introduce the notion of a tensor invariant under a derivation on an ideal of $A$. Each system of partial differential equations generates an ideal in some differential algebra. This makes it possible to study invariant tensors on such an ideal. As examples we consider the equations of gas dynamics and magnetohydrodynamics.