Theorems · Theorem · commutative algebra
Algebra.FinitePresentation.ker_fg_of_mvPolynomial
∀ {R : Type w₁} {A : Type w₂} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {n : ℕ}
(f : MvPolynomial (Fin n) R →ₐ[R] A),
Function.Surjective ⇑f → ∀ [Algebra.FinitePresentation R A], (RingHom.ker f.toRingHom).FGThis is used to prove the strictly stronger ker_fg_of_surjective. Use it instead.
- Defined in
- Mathlib.RingTheory.FinitePresentation
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites70
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Finsuppstatement · cited by 5,255
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FinitePresentation.ker_fG_of_surjectiveproof · cited by 7