Theorems · Definition · commutative algebra
ClassGroup.mk0
{R : Type u_1} →
[inst : CommRing R] → [inst_1 : IsDomain R] → [IsDedekindDomain R] → ↥(nonZeroDivisors (Ideal R)) →* ClassGroup RSend a nonzero ideal to the corresponding class in the class group.
- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement · cited by 895
- IsDedekindDomainstatement and proof · cited by 668
- MonoidHom.compproof · cited by 469
- FractionRingproof · cited by 200
- ClassGroupstatement · cited by 50
- ClassGroup.mkproof · cited by 22
- FractionalIdeal.mk0proof · cited by 13
Cited by23
Results whose statement or proof uses this declaration.
- ClassGroup.mk0_surjectivestatement · cited by 5
- ClassGroup.mk0_eq_one_iffstatement · cited by 4
- ClassGroup.mk_mk0statement · cited by 3
- NumberField.Ideal.tendsto_norm_le_div_atTop₀proof · cited by 2
- RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_norm_leproof · cited by 2
- ClassGroup.extendedHom_mk0statement and proof · cited by 2
- card_classGroup_eq_one_iffproof · cited by 2
- ClassGroup.mkMMemproof · cited by 1
- NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTopstatement and proof · cited by 1
- ClassGroup.equiv_mk0statement · cited by 1
- ClassGroup.exists_mk0_eq_mk0statement and proof · cited by 1
- ClassGroup.extendedHom_comp_applyproof · cited by 1