  We propose a new algebraic approach to study compatibility of partial
differential equations. The approach uses concepts from commutative algebra,
algebraic geometry and Gr\"obner bases to clarify crucial notions concerning
compatibility such as passivity (involution) and reducibility. One obtains
sufficient conditions for a differential system to be passive and prove that
such systems generate manifolds in the jet space. Some examples of
constructions of passive systems associated with the sinh-Gordon equation are
given.
