Theorems · Theorem · commutative algebra
ClassGroup.mk0_eq_mk0_inv_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)⁻¹ ↔ ∃ x, x ≠ 0 ∧ ↑I * ↑J = Ideal.span {x}- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- Submodule.spanproof · cited by 1,504
- map_mulproof · cited by 1,137
- Ideal.spanstatement and proof · cited by 948
- nonZeroDivisorsstatement and proof · cited by 895
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.exists_ideal_in_class_of_norm_leproof · cited by 1