Theorems · Theorem · commutative algebra
AlgHom.ker_kerSquareLift
∀ {R : Type u} [inst : CommRing R] {A : Type u_1} {B : Type u_2} [inst_1 : CommRing A] [inst_2 : CommRing B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₐ[R] B),
RingHom.ker f.kerSquareLift.toRingHom = (RingHom.ker f.toRingHom).cotangentIdeal- Defined in
- Mathlib.RingTheory.Ideal.Cotangent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Idealstatement · cited by 4,748
- AlgHomstatement and proof · cited by 3,236
- HasQuotient.Quotientstatement and proof · cited by 2,301
- le_antisymmproof · cited by 2,068
- Ideal.Quotient.mkproof · cited by 610
- AlgHom.toRingHomstatement and proof · cited by 490
- RingHom.kerstatement and proof · cited by 363
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.of_comp_surjectiveproof · cited by 6
- Algebra.FormallyUnramified.iff_comp_injective_of_smallproof · cited by 4
- Algebra.Extension.ker_infinitesimalproof · cited by 1