Theorems · Theorem · commutative algebra
ClassGroup.equiv_mk0
∀ {R : Type u_1} (K : Type u_2) [inst : CommRing R] [inst_1 : Field K] [inst_2 : Algebra R K]
[inst_3 : IsFractionRing R K] [inst_4 : IsDomain R] [inst_5 : IsDedekindDomain R] (I : ↥(nonZeroDivisors (Ideal R))),
(ClassGroup.equiv K) (ClassGroup.mk0 I) = (QuotientGroup.mk' (toPrincipalIdeal R K).range) ((FractionalIdeal.mk0 K) I)- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientstatement and proof · cited by 2,301
- IsDomainstatement and proof · cited by 2,196
- MulEquivstatement · cited by 1,142
Cited by1
Results whose statement or proof uses this declaration.
- ClassGroup.mk0_eq_mk0_iff_exists_fraction_ringproof · cited by 1