Theorems · Theorem · commutative algebra
ClassGroup.mk_def
∀ {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] (I : (FractionalIdeal (nonZeroDivisors R) K)ˣ),
(ClassGroup.mk K) I =
(QuotientGroup.mk' (toPrincipalIdeal R (FractionRing R)).range)
((Units.map ↑(FractionalIdeal.canonicalEquiv (nonZeroDivisors R) K (FractionRing R))) I)- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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 · cited by 3,629
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientstatement · cited by 2,301
- IsDomainstatement and proof · cited by 2,196
- RingEquivstatement · cited by 1,147
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
Cited by4
Results whose statement or proof uses this declaration.
- ClassGroup.Quot_mk_eq_mkproof · cited by 3
- ClassGroup.mk_eq_mkproof · cited by 2
- ClassGroup.equiv_mkproof · cited by 2
- ClassGroup.mk_canonicalEquivproof · cited by 1