11 Let be an ideal of forms on M locally generated by r independent 1-forms. Say S is generated by ,,...,W, on U. Then the condi- tion that be a differential ideal is equivalent to each of: (a) dw, - Ew, Aw, for some 1-forms w. (for each such (UW,...,w.)). (b) If w A... AW, then dwa w for some 1-forma (for each such (U,,,...,w.)). 11 Let be an ideal of forms on M locally generated by r independent 1-forms. Say S is generated by ,,...,W, on U. Then the condi- tion that be a differential ideal is equivalent to each of: (a) dw, - Ew, Aw, for some 1-forms w. (for each such (UW,...,w.)). (b) If w A... AW, then dwa w for some 1-forma (for each such (U,,,...,w.))