Theorems · Definition · commutative algebra
ClassGroup.equivPic
(R : Type u_5) → [inst : CommRing R] → [inst_1 : IsDomain R] → ClassGroup R ≃* CommRing.Pic R
The class group of a domain is isomorphic to the Picard group.
- Defined in
- Mathlib.RingTheory.PicardGroup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsDomainstatement and proof · cited by 2,196
- MulEquivstatement · cited by 1,142
- FractionRingproof · cited by 200
- MulEquiv.transproof · cited by 53
- ClassGroupstatement · cited by 50
- CommRing.Picstatement · cited by 37
- MulEquiv.subgroupCongrproof · cited by 10
- Subgroup.topEquivproof · cited by 10
- ClassGroup.mulEquivUnitsSubmoduleQuotRangeproof · cited by 2
- Submodule.unitsQuotEquivRelPicproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ClassGroup.equivPic_applystatement and proof · cited by 0
- ClassGroup.equivPic_symm_applystatement and proof · cited by 0