Theorems · Theorem · commutative algebra
ClassGroup.equiv_mk
∀ {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] (K' : Type u_3) [inst_5 : Field K'] [inst_6 : Algebra R K']
[inst_7 : IsFractionRing R K'] (I : (FractionalIdeal (nonZeroDivisors R) K)ˣ),
(ClassGroup.equiv K') ((ClassGroup.mk K) I) =
(QuotientGroup.mk' (toPrincipalIdeal R K').range)
((Units.mapEquiv ↑(FractionalIdeal.canonicalEquiv (nonZeroDivisors R) K K')) I)- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientstatement and proof · cited by 2,301
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- RingEquivstatement · cited by 1,147
- MulEquivstatement and proof · cited by 1,142
Cited by2
Results whose statement or proof uses this declaration.
- ClassGroup.mk_eq_one_iffproof · cited by 4
- ClassGroup.equiv_mk0proof · cited by 1