Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.comp_injective
∀ {R : Type v} [inst : CommRing R] {A : Type u} [inst_1 : CommRing A] [inst_2 : Algebra R A] {B : Type w}
[inst_3 : CommRing B] [inst_4 : Algebra R B] (I : Ideal B) [Algebra.FormallyUnramified R A],
I ^ 2 = ⊥ → Function.Injective (Ideal.Quotient.mkₐ R I).comp- Defined in
- Mathlib.RingTheory.Unramified.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- IsScalarTowerproof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AlgHom.compstatement and proof · cited by 501
- AlgHom.toRingHomproof · cited by 490
- RingHom.toAlgebraproof · cited by 337
- Equiv.transproof · cited by 337
- IsScalarTower.toAlgHomproof · cited by 232
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.of_equivproof · cited by 4
- Algebra.FormallyUnramified.of_surjectiveproof · cited by 4
- Algebra.FormallyUnramified.iff_comp_injective_of_smallproof · cited by 4
- Algebra.FormallyUnramified.lift_uniqueproof · cited by 3
- Algebra.FormallySmooth.of_restrictScalarsproof · cited by 2
- Algebra.FormallyEtale.comp_bijectiveproof · cited by 2
- Algebra.FormallyUnramified.pi_iffproof · cited by 1