**Geometric Interpretation**

The ideal quotient corresponds to set difference in algebraic geometry. More precisely,

- If
*W*is an affine variety and*V*is a subset of the affine space (not necessarily a variety), then

*I*(*V*) :*I*(*W*) =*I*(*V**W*),

where *I* denotes the taking of the ideal associated to a subset.

- If
*I*and*J*are ideals in*k*, then

*Z*(*I*:*J*) = cl(*Z*(*I*)*Z*(*J*))

where "cl" denotes the Zariski closure, and *Z* denotes the taking of the variety defined by the ideal *I*.

Read more about this topic: Ideal Quotient

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### Famous quotes containing the word geometric:

“New York ... is a city of *geometric* heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation.”

—Roland Barthes (1915–1980)