Theorems · Theorem · commutative algebra
ClassGroup.Quot_mk_eq_mk
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R]
(I : (FractionalIdeal (nonZeroDivisors R) (FractionRing R))ˣ),
Quot.mk (⇑(QuotientGroup.leftRel (toPrincipalIdeal R (FractionRing R)).range)) I = (ClassGroup.mk (FractionRing R)) I- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 3 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.
Cites24
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
- MonoidHomstatement and proof · cited by 3,629
- Unitsstatement and proof · cited by 2,804
- HasQuotient.Quotientproof · cited by 2,301
- IsDomainstatement and proof · cited by 2,196
- RingEquivproof · cited by 1,147
- nonZeroDivisorsstatement and proof · cited by 895
- FractionalIdealstatement and proof · cited by 423
- MonoidHom.rangestatement and proof · cited by 314
- MonoidHomClass.toMonoidHomproof · cited by 294
- FractionRingstatement and proof · cited by 200
Cited by3
Results whose statement or proof uses this declaration.
- ClassGroup.mk0_surjectiveproof · cited by 5
- ClassGroup.extendedHom_mkproof · cited by 1
- ClassGroup.mk0_eq_quotientMkproof · cited by 1