Theorems · Theorem · number theory
Ideal.quotientToQuotientRangePowQuotSucc_injective
Deprecated since 2026-07-01Mathlib marks this declaration as deprecated.
∀ {R : Type u} [inst : CommRing R] {S : Type v} [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R) (P : Ideal S)
[hfp : NeZero (p.ramificationIdx' P)] [IsDedekindDomain S] [P.IsPrime] {i : ℕ},
i < p.ramificationIdx' P →
∀ {a : S} (a_mem : a ∈ P ^ i), a ∉ P ^ (i + 1) → Function.Injective ⇑(p.quotientToQuotientRangePowQuotSucc P a_mem)- Cited by
- 0 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.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- LinearMap.rangestatement and proof · cited by 893
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement and proof · cited by 692
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.