Mathlib Map

Theorems · Definition · commutative algebra

ClassGroup.mk0

{R : Type u_1} →
  [inst : CommRing R] → [inst_1 : IsDomain R] → [IsDedekindDomain R] → ↥(nonZeroDivisors (Ideal R)) →* ClassGroup R

Send 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
Assumes
CommRingIsDomainIsDedekindDomain

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ClassGroup.mk0_surjective · cited by 5ClassGroup.mk0_surjectiveClassGroup.mk0_eq_one_iff · cited by 4ClassGroup.mk0_eq_one_iffClassGroup.mk_mk0 · cited by 3ClassGroup.mk_mk0NumberField.Ideal.tendsto_norm_le_div_atTop₀ · cited by 2Ideal.tendsto_norm_le_div…RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_norm_le · cited by 2RingOfIntegers.isPrincipa…ClassGroup.extendedHom_mk0 · cited by 2ClassGroup.extendedHom_mk0card_classGroup_eq_one_iff · cited by 2card_classGroup_eq_one_iffClassGroup.mkMMem · cited by 1ClassGroup.mkMMemNumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop · cited by 1Ideal.tendsto_norm_le_and…ClassGroup.equiv_mk0 · cited by 1ClassGroup.equiv_mk0ClassGroup.exists_mk0_eq_mk0 · cited by 1ClassGroup.exists_mk0_eq_…ClassGroup.extendedHom_comp_apply · cited by 1ClassGroup.extendedHom_co…NumberField.exists_ideal_in_class_of_norm_le · cited by 1NumberField.exists_ideal_…ClassGroup.mk0_eq_mk0_iff · cited by 1ClassGroup.mk0_eq_mk0_iffClassGroup.mk0_eq_mk0_iff_exists_fraction_ring · cited by 1ClassGroup.mk0_eq_mk0_iff…CommRing · cited by 17173CommRingIdeal · cited by 4748IdealMonoidHom · cited by 3629MonoidHomSubmonoid · cited by 3086SubmonoidIsDomain · cited by 2196IsDomainnonZeroDivisors · cited by 895nonZeroDivisorsIsDedekindDomain · cited by 668IsDedekindDomainMonoidHom.comp · cited by 469MonoidHom.compFractionRing · cited by 200FractionRingClassGroup · cited by 50ClassGroupClassGroup.mk · cited by 22ClassGroup.mkFractionalIdeal.mk0 · cited by 13FractionalIdeal.mk0ClassGroup.mk0CITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by23

Results whose statement or proof uses this declaration.