A differential ideal 
on a manifold 
is an ideal in the exterior
algebra of differential k-forms
on 
which is also closed under the exterior
derivative 
.
That is, for any differential k-form 
and any form 
,
1. 
,
and
2. 
.
For example, 
is a differential ideal on 
.
A smooth map 
is called an integral of 
if the pullbacks of all forms in 
vanish on 
, i.e., 
.
