Theorems · Theorem · commutative algebra
ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring
∀ {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] [inst_5 : IsDedekindDomain R]
{I J : ↥(nonZeroDivisors (Ideal R))},
ClassGroup.mk0 I = ClassGroup.mk0 J ↔
∃ x, ∃ (_ : x ≠ 0), FractionalIdeal.spanSingleton (nonZeroDivisors R) x * ↑↑I = ↑↑J- 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.
Cites28
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
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- Unitsproof · cited by 2,804
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- nonZeroDivisorsstatement and proof · cited by 895
Cited by1
Results whose statement or proof uses this declaration.
- ClassGroup.mk0_eq_mk0_iffproof · cited by 1