Theorems · Theorem · algebraic geometry
MvPolynomial.eq_vanishingIdeal_singleton_of_isMaximal
∀ {k : Type u_1} (K : Type u_2) [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k 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
- 2 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Finsuppstatement · cited by 5,255
- Idealstatement and proof · cited by 4,748
- AlgHomproof · cited by 3,236
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientproof · cited by 2,301
- MvPolynomialstatement and proof · cited by 2,140
- Ideal.Quotient.mkproof · cited by 610
- MvPolynomial.Xproof · cited by 552
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.vanishingIdeal_zeroLocus_eq_radicalproof · cited by 1
- MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singletonproof · cited by 0