Theorems · Theorem · commutative algebra
ClassGroup.mk0_eq_mk0_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDedekindDomain R]
{I J : ↥(nonZeroDivisors (Ideal R))},
ClassGroup.mk0 I = ClassGroup.mk0 J ↔ ∃ x y, ∃ (_ : x ≠ 0) (_ : y ≠ 0), Ideal.span {x} * ↑I = Ideal.span {y} * ↑J- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 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 and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- Ideal.spanstatement and proof · cited by 948
- nonZeroDivisorsstatement and proof · cited by 895
Cited by1
Results whose statement or proof uses this declaration.
- ClassGroup.exists_mk0_eq_mk0proof · cited by 1