For an algebraically-closed field k and an ideal J ⊆ k[x₁,…,x_n]: I(V(J)) = √J, the radical of J. In particular, V(J) = ∅ iff 1 ∈ J, and maximal ideals of k[x₁,…,x_n] are exactly the evaluation ideals m_p = (x₁ − a₁,…,x_n − a_n) for…
For an algebraically-closed field k and an ideal J ⊆ k[x₁,…,x_n]: I(V(J)) = √J, the radical of J. In particular, V(J) = ∅ iff 1 ∈ J, and maximal ideals of k[x₁,…,x_n] are exactly the evaluation ideals m_p = (x₁ − a₁,…,x_n − a_n) for…