Theorems · Definition · commutative algebra
ClassGroup.mulEquiv
{R : Type u_1} →
[inst : CommRing R] →
[inst_1 : IsDomain R] →
{R' : Type u_3} → [inst_2 : CommRing R'] → [inst_3 : IsDomain R'] → R ≃+* R' → ClassGroup R ≃* ClassGroup R'A ring isomorphism R ≃+* R' induces an isomorphism on their class groups.
- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 2 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.
Cites15
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
- RingEquivstatement and proof · cited by 1,147
- MulEquivstatement · cited by 1,142
- MulEquiv.symmproof · cited by 482
- MonoidHom.rangeproof · cited by 314
- FractionRingproof · cited by 200
- MulEquivClass.toMulEquivproof · cited by 57
- MulEquiv.transproof · cited by 53
- ClassGroupstatement · cited by 50
- toPrincipalIdealproof · cited by 23
- QuotientGroup.congrproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- ClassGroup.mulEquiv_applystatement and proof · cited by 0
- ClassGroup.mulEquiv_symm_applystatement and proof · cited by 0