Theorems · Theorem · algebraic geometry
MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton
∀ {K : Type u_2} [inst : Field K] {σ : Type u_3} [IsAlgClosed K] [Finite σ] {I : Ideal (MvPolynomial σ K)},
I.IsMaximal ↔ ∃ x, I = MvPolynomial.vanishingIdeal K {x}- Defined in
- Mathlib.RingTheory.Nullstellensatz
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsAlgClosedFinite
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Finsuppstatement · cited by 5,255
- Idealstatement and proof · cited by 4,748
- Finitestatement and proof · cited by 3,029
- MvPolynomialstatement and proof · cited by 2,140
- Ideal.IsMaximalstatement and proof · cited by 452
- IsAlgClosedstatement and proof · cited by 150
- MvPolynomial.vanishingIdealstatement and proof · cited by 14
- MvPolynomial.eq_vanishingIdeal_singleton_of_isMaximalproof · cited by 2
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