Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.iff_comp_injective_of_small
∀ {R : Type v} [inst : CommRing R] {A : Type u} [inst_1 : CommRing A] [inst_2 : Algebra R A] [Small.{w, u} A],
Algebra.FormallyUnramified R A ↔
∀ ⦃B : Type w⦄ [inst_4 : CommRing B] [inst_5 : Algebra R B] (I : Ideal B),
I ^ 2 = ⊥ → Function.Injective (Ideal.Quotient.mkₐ R I).comp- Defined in
- Mathlib.RingTheory.Unramified.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites48
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
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Equiv.symmproof · cited by 3,681
- AlgHomstatement and proof · cited by 3,236
- TensorProductproof · cited by 2,545
- HasQuotient.Quotientstatement and proof · cited by 2,301
- RingHomClass.toRingHomproof · cited by 746
- Ideal.mapproof · cited by 692
- AlgEquiv.symmproof · cited by 615
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.iff_comp_injectiveproof · cited by 8
- Algebra.FormallyEtale.of_isSeparableproof · cited by 3
- Algebra.FormallyEtale.iff_comp_bijectiveproof · cited by 2
- Algebra.FormallyEtale.of_isSeparable_auxproof · cited by 1