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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