Theorems · Theorem · commutative algebra
Algebra.FinitePresentation.out
∀ {R : Type w₁} {A : Type w₂} {inst : CommSemiring R} {inst_1 : Semiring A} {inst_2 : Algebra R A}
[self : Algebra.FinitePresentation R A], ∃ n f, Function.Surjective ⇑f ∧ (RingHom.ker f.toRingHom).FG- Defined in
- Mathlib.RingTheory.FinitePresentation
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Algebra.FinitePresentation
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Finsuppstatement · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- AlgHom.toRingHomstatement · cited by 490
- RingHom.kerstatement · cited by 363
- Ideal.FGstatement · cited by 99
- Algebra.FinitePresentationstatement and proof · cited by 56
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.FinitePresentation.equivproof · cited by 9
- Algebra.FinitePresentation.ker_fG_of_surjectiveproof · cited by 7
- Algebra.FinitePresentation.quotientproof · cited by 3
- Algebra.FinitePresentation.of_restrict_scalars_finitePresentationproof · cited by 2
- Algebra.FinitePresentation.ker_fg_of_mvPolynomialproof · cited by 1
- Algebra.Presentation.exists_presentation_finproof · cited by 0