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 *d*α 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.

Read more about Differential Ideal: Exterior Differential Systems and Partial Differential Equations, Perfect Differential Ideals

### Other articles related to "differential ideal":

**Differential Ideal**s

... a

**differential ideal**which has the property that if it contains an element they contain any element such that for some is equal to ...

### Famous quotes containing the words ideal and/or differential:

“It is equally impossible to forget our Friends, and to make them answer to our *ideal*. When they say farewell, then indeed we begin to keep them company. How often we find ourselves turning our backs on our actual Friends, that we may go and meet their *ideal* cousins.”

—Henry David Thoreau (1817–1862)

“But how is one to make a scientist understand that there is something unalterably deranged about *differential* calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”

—Antonin Artaud (1896–1948)