Theorems · Theorem · commutative algebra
Algebra.Generators.ker_eq_ker_aeval_val
∀ {R : Type u} {S : Type v} {ι : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : Algebra.Generators R S ι), P.ker = RingHom.ker (MvPolynomial.aeval P.val)- Defined in
- Mathlib.RingTheory.Extension.Generators
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Finsuppstatement · cited by 5,255
- Idealstatement · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- RingHomClass.toRingHomproof · cited by 746
- RingHom.kerstatement and proof · cited by 363
- MvPolynomial.aevalstatement and proof · cited by 298
- Algebra.Extension.Ringproof · cited by 179
- Algebra.Generatorsstatement and proof · cited by 152
Cited by13
Results whose statement or proof uses this declaration.
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Algebra.Presentation.aeval_val_relationproof · cited by 5
- Algebra.Generators.map_ofComp_kerproof · cited by 3
- Algebra.Generators.map_toComp_kerproof · cited by 3
- Algebra.Generators.exists_presentation_of_basis_cotangentproof · cited by 2
- Algebra.SubmersivePresentation.cotangentComplexAux_injectiveproof · cited by 1
- Algebra.Generators.H1Cotangent.liftBaseChange_range_leproof · cited by 1
- Algebra.Generators.fg_ker_of_finitePresentationproof · cited by 1
- Algebra.Generators.ker_comp_eq_supproof · cited by 1
- Algebra.Generators.ker_localizationAwayproof · cited by 1
- Algebra.Presentation.span_range_relation_eq_ker_compproof · cited by 0
- Algebra.Generators.ker_mvPolynomialproof · cited by 0