In the theory of differential forms, a differential ideal I is an algebraic ideal in the ring of smooth differential forms on a smooth manifold, in other words a graded ideal in the sense of ring theory, that is further closed under exterior differentiation d. In other words, for any form α in I, the exterior derivative dα is also in I. In the theory of differential algebra, a differential ideal I in a differential ring R is an ideal which is mapped to itself by each differential operator.