  We consider a differential algebra F of formal power series in infinitely
many variables. We define the important notions of a normalized set of
generators for an ideal of F and a regular quotient algebra. The concept of the
passive collection being analog of involutive system of the nonlinear partial
differential equations and Gr\"obner basis is introduced. Using special
partitions of the algebra F and action of a semigroup on F, the sufficient
conditions of passivity are obtained. The proof of the main theorem essentially
differs from similar one for the differential equations and we obtain more
general statement.
