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**Trivial (!?) alg. geometry problem**

## Homework Statement

Consider [tex]Y=Q_1,Q_2,\ldots,Q_r \subset \mathbb{A}^n [/tex], a finite set of [tex] r [/tex] different points. What are the generators of the ideal [tex]I(Y)[/tex]

## The Attempt at a Solution

Knowing that [tex] I(Q_i)=(X_1-Q_{i,1},\ldots,X_n-Q_{i,n}) [/tex] and so on, my guess would be that the solution is something like

[tex] (\prod_{k=1}^r f_{k,i}), 1 \leq i \leq n [/tex] with [tex]f_{k,i} \in I(Q_k) [/tex]

It seems kind of messed. Any ideas?