Theorems · Theorem · commutative algebra
ClassGroup.mk0_eq_quotientMk
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDedekindDomain R]
(I : ↥(nonZeroDivisors (Ideal R))), ClassGroup.mk0 I = ↑((FractionalIdeal.mk0 (FractionRing R)) I)ClassGroup.mk0 factors through the canonical quotient projection on
(FractionalIdeal R⁰ (FractionRing R))ˣ.
- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- Unitsstatement · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- IsDedekindDomainstatement and proof · cited by 668
- FractionalIdealstatement · cited by 423
- MonoidHom.rangestatement · cited by 314
- FractionRingstatement and proof · cited by 200
Cited by1
Results whose statement or proof uses this declaration.
- ClassGroup.extendedHom_mk0proof · cited by 2