  An algebraic technique is presented that does not use results of model theory
and makes it possible to construct a general Galois theory of arbitrary
nonlinear systems of partial differential equations. The algebraic technique is
based on the search for prime differential ideals of special form in tensor
products of differential rings. The main results demonstrating the work of the
technique obtained are the theorem on the constructedness of the differential
closure and the general theorem on the Galois correspondence for normal
extensions..
